A defining property of Hawking radiation is that states with very low entanglement masquerade as highly mixed states; this property is captured by a quantum computational phenomenon known as spoofing entanglement. Motivated by the potential implications for black hole information and the emergence of spacetime connectivity, as well as possible applications of spoofing entanglement, we investigate the geometrization of two types of entanglement spoofers in AdS/CFT: so-called EFI pairs and pseudoentangled state ensembles. We show that (a strengthened version of) EFI pairs with a semiclassical bulk dual have a Python's Lunch; the maximally mixed state over the pseudoentangled state ensemble likewise features a Python's Lunch. Since a Python's Lunch must lie behind an event horizon, we find that black holes are the exclusive gravitational source of entanglement spoofing in the semiclassical limit. Finally, we use an extant construction of holographic pseudorandom states to yield a candidate example of a pseudoentangled state ensemble with a semiclassical bulk dual.

We study conformal field theories at finite temperature in the presence of a temporal conformal line defect, wrapping the thermal circle, akin to a Polyakov loop in gauge theories. Although several symmetries of the conformal group are broken, the model can still be highly constrained from its features at zero-temperature. In this work we show that the defect and bulk one and two-point correlators can be written as functions of zero-temperature data and thermal one-point functions (defect and bulk). The defect one-point functions are new data and they are induced by thermal effects of the bulk. For this new set of data we derive novel sum rules and establish a bootstrap problem for the thermal defect one-point functions from the KMS condition. We also comment on the behaviour of operators with large scaling dimensions. Additionally, we relate the free energy and entropy density to the OPE data through the one-point function of the stress-energy tensor. Our formalism is validated through analytical computations in generalized free scalar field theory, and we present new predictions for the O(N) model with a magnetic impurity in the $\varepsilon$-expansion and the large N limit.

We investigate the geometrical structure of multiply enhanced codimension-two singularities in the $SU(5)$ model of six-dimensional F-theory, where the rank of the singularity increases by two or more. We perform blow-up processes for the enhancement $SU(5)\rightarrow G'$, where $G'=E_6$, $E_7$ or $E_8$, to examine whether a sufficient set of exceptional curves emerge that can explain the charged matter generation predicted from anomaly cancelation. We first apply one of the six Esole-Yau small resolutions to the multiply enhanced singularities, but it turns out that the proper transform of the threefold equation does not reflect changes in the singularity or how the generic codimension-two singularities gather there. We then use a(n) (apparently) different way of small resolutions than Esole-Yau to find that, except for the cases of $G'= E_6$ and special cases of $E_7$, either (1) the resolution only yields exceptional curves that are insufficient to cancel the anomaly, or (2) there arises a type of singularity that is neither a conifold nor a generalized conifold singularity. Finally, we revisit the Esole-Yau small resolution and show that the change of the way of small resolutions amounts to simply exchanging the proper transform and the constraint condition, and under this exchange the two ways of small resolutions are completely equivalent.

We study the correlation functions of local operators in unitary $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation function in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation function is computed and compared to that of $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a plane. For the latter, the behavior found was $|q|^{-\frac{tq^2}{\pi}}$, where $q$ is the momentum and $t$ is the deformation parameter. For a torus, the same behavior is found for $|q|<<L/t$, where $L$ is the torus' length scale. However, for $|q|>>L/t$, a different behavior is found: $\left(\frac{4\sqrt{t}^5q^2}{\pi e L^3|T|^2}\right)^{\frac{tq^2}{\pi}}$, where $T$ is the modular parameter of the torus. Hence, at large momentum, the correlator decays and then grows. This behavior suggests that operators carrying momentum $q$ are smeared on a distance scale $t|q|$. The difference from the plane's result illustrates the non-locality of the theory and the UV-IR mixing.

We study integrability and non-integrability of non-SUSY quivers in 4d that are dual to marginal deformations of Gaiotto-Maldacena geometry in 10d. We explore the dual operator spectrum and the fate of Liouvillian non-integrability both in the presence and the absence of the flavour degrees of freedom. We also comment about the factorised scattering and the associated integrability or non-integrability of the sigma model. Our analysis reveals the mutual compatibility between two seemingly different approaches that has existed in the literature for a long time.

Here, we explore the formation of primordial black holes (PBHs) within a scalar field inflationary model coupled to the Gauss-Bonnet (GB) term, incorporating low-scale spontaneously broken supersymmetric (SB SUSY) potential. The coupling function amplifies the curvature perturbations, consequently leading to the formation of PBHs and the production of detectable secondary gravitational waves (GWs). Through the adjustment of model parameters, the inflaton can be decelerated during the ultra-slow-roll (USR) phase, thereby augmenting curvature perturbations. Swampland criteria are also investigated. Our computations forecast the formation of PBHs with masses on the order of ${\cal O}(10)M_{\odot}$, aligning with observational data from LIGO-Virgo and PBHs with masses ${\cal O}(10^{-6})M_{\odot}$, offering potential explanation for ultrashort-timescale microlensing events recorded in OGLE data. Additionally, our proposed mechanism can generate PBHs with masses around ${\cal O}(10^{-13})M_{\odot}$, constituting roughly 99$\%$ of the dark matter. The density parameter of produced GWs ($\Omega_{\rm GW_0}$) intersects with the sensitivity curves of GW detectors. Two cases of our model fall within the nano-Hz regime. One of these satisfies the $\Omega_{\rm{GW}}(f) \sim f^{5-\gamma}$ fit, with the derived $\gamma = 3.51$ matching the NANOGrav 15-year data.

An algebraic characterization of the contractions of the Poincar\'e group permits a proper construction of a non-relativistic limit of its tachyonic representation. We arrive at a consistent, nonstandard representation of the Galilei group which was disregarded long ago by supposedly unphysical properties. The corresponding quantum (and classical) theory shares with the relativistic one their fundamentals, and serves as a toy model to better comprehend the unusual behavior of the tachyonic representation. For instance, we see that evolution takes place in a spatial coordinate rather than time, as for relativistic tachyons, but the modulus of the three-momentum is the same for all Galilean observers, leading to a new dispersion relation for a Galilean system. Furthermore, the tachyonic objects described by the new representation cannot be regarded as localizable in the standard sense.

The center-of-mass energy of two colliding particles could be arbitrarily high in the vicinity of event horizons of the extremal Myers-Perry black holes if the angular momentum of colliding particles is fine-tuned to the critical values. We investigate the maximum efficiency of two colliding particles in four and six dimensions. The efficiency of collision for two particles near the four-dimensional Kerr black holes is 130 %. We show that the efficiency increases to 145 % for collision in six dimensions. We also show that the region for the polar angle in which the particle can reach the high energy is larger when the dimension of space-time increases.

The tensionless string on AdS$_3$ is a laboratory to study different aspects of the AdS/CFT correspondence. A particular question addressed in this paper is how the space-time symmetry algebra is encoded on the world-sheet. A natural prescription for calculating the space-time OPEs from the world-sheet is presented in the hybrid formalism. An argument showing that the OPEs are correctly reproduced from the world-sheet is provided, together with a few explicit calculations as consistency checks.

We describe a one-parameter family of Euclidean wormhole solutions with the topology of a compact hyperbolic space times an interval in Einstein gravity minimally coupled to a massless scalar field in AdS$_{d+1}$ commonly referred to as Einstein-dilaton gravity. These solutions are locally described by the same metric and dilaton profile as the single-boundary Janus domain wall solutions in the same theory which are usually studied in the context of holographic RG flows. The wormholes compute the averaged product of partition functions of CFTs on either boundary deformed by different marginal couplings to the scalar operator dual to the dilaton. We observe that the renormalised volumes of these wormholes increase monotonically with the difference in the marginal couplings on the boundary thereby showing that the pair of CFTs on the boundaries get increasingly decorrelated as the difference in the marginal couplings increases. We use the partition functions of the three-dimensional wormhole solutions to determine the variance of the OPE data of local operators between the marginally deformed 2d CFTs and quantify how the variance decays with the difference in marginal couplings. In addition, a family of wormholes sourced by a thin shell of dust determine how the variance of the matrix elements of the dual line defect decays with the difference in marginal couplings. Applying the GKPW dictionary to wormholes, we compute averages of integrated dilaton correlators treating the wormhole amplitude as a functional of the dilaton sources. We observe that the crossed two-point correlators with a dilaton insertion on either boundary decay montonically with the difference in marginal couplings consistent with the observation that the CFTs increasingly decorrelate as the difference in marginal couplings grows.

In the context of four-dimensional ${\cal N} = 1$ type IIB superstring compactifications, the U-dual completion of the holomorphic flux superpotential leads to four S-dual pairs of fluxes, namely $(F, H), (Q, P), (P', Q')$ and $(H', F')$. It has been observed that the scalar potentials induced by such generalized superpotentials typically have an enormous amount of terms, making it hard to study any phenomenological aspects such as moduli stabilization. In this regard, we present a set of generic master formulae which not only formulate the scalar potential in a compact way but also enable one to {\it read-off} the various scalar potential pieces by simply knowing a set of topological data of the compactifying Calabi Yau and its mirror threefold. We demonstrate the applicability of our master formulae by {\it reading-off} the scalar potentials for five explicit models, and using a set of {\it axionic flux} combinations we show that 76276 terms arising from the flux superpotential in a ${\mathbb T}^6/({\mathbb Z}_2\times{\mathbb Z}_2)$-based model can be equivalently expressed by using 2816 terms, while 11212 terms arising from the flux superpotential in a Quintic-based model can be equivalently expressed by 668 terms! We argue that the master formulae presented in this work can be useful in an analytic exploration of the rich landscape of the non-geometric flux vacua.

Based on a recently proposed quantum field theory (QFT) for particles with or without structure, called "Structural Algebraic QFT (SAQFT)", we introduce a finite QFT. That is, a QFT for structureless elementary particles that does not require renormalization where loop integrals in the Feynman diagrams are finite. It is an algebraic theory utilizing orthogonal polynomials and based on the structureless sector of SAQFT.

We construct the gravitational energy-momentum pseudo-tensor of up to fourth-order conformally invariant theories of gravity. Then we linearize the pseudo-tensor and use its average over a macroscopic region to find the energy and momentum carried by the plane gravitational waves of the three main conformally invariant theories of gravity.

In this work, we consider the corrections to the cosmological models based on the teleparallel equivalent of general relativity induced by the non-minimal coupling between scalar field and torsion. To determine these corrections, we consider a power-law parametrization of the deviations between the teleparallel equivalent of general relativity and the scalar-torsion gravity. The estimates of the possible influence of the non-minimal coupling of the scalar field and torsion on the background cosmological parameters and the parameters of cosmological perturbations for the inflationary models implying linear relation between tensor-to-scalar ratio and spectral index of the scalar perturbations are obtained. A procedure for verifying these inflationary models based on observational constraints on the values of cosmological perturbation parameters is also considered.

We present analytic results for three-loop fermionic corrections to the heavy-light form factors in perturbative quantum chromodynamics. Specifically, we present all light quark contributions and contributions from two heavy quark loops. We use the method of differential equations to compute all relevant three-loop master integrals. The results for all these contributions are expressed in terms of harmonic polylogarithms and generalized harmonic polylogarithms.

In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional first derivatives and fractional linear momenta, similarly to classical mechanics. We derive the corresponding equations of motion and explore the symmetries of the model. Also, we present the formulation in terms of fractional potentials. Two important examples are analytically solved: the free particle and the particle subjected to generalized forces characterized by fractional first derivatives.

We introduce a class of multi-Higgs doublet extensions of the Standard Model that solves the strong CP problem with profound consequences for the flavor sector. The Yukawa matrices are constrained to have many zero entries by a "Higgs-Flavor" symmetry, $G_{\rm HF}$, that acts on Higgs and quark fields. The violation of both CP and $G_{\rm HF}$ occurs in the Higgs mass matrix so that, for certain choices of $G_{\rm HF}$ charges, the strong CP parameter $\bar{\theta}$ is zero at tree-level. Radiative corrections to $\bar{\theta}$ are computed in this class of theories. They vanish in realistic two-Higgs doublet models with $G_{\rm HF} = \mathbb{Z}_3$. We also construct realistic three-Higgs models with $G_{\rm HF} = \rm U(1)$, where the one-loop results for $\bar{\theta}$ are model-dependent. Requiring $\bar{\theta}< 10^{-10}$ has important implications for the flavor problem by constraining the Yukawa coupling and Higgs mass matrices. Contributions to $\bar{\theta}$ from higher-dimension operators are computed at 1-loop and can also be sufficiently small, although the hierarchy problem of this class of theories is worse than in the Standard Model.

We study the All-Line Transverse (ALT) shift which we developed for on-shell recursion of amplitudes for particles of any mass. We discuss the validity of the shift for general theories of spin $\leq$ 1, and illustrate the connection between Ward identity and constructibility for massive spin-1 amplitude under the ALT shift. We apply the shift to the electroweak theory, and various four-point scattering amplitudes among electroweak gauge bosons and fermions are constructed. We show explicitly that the four-point gauge boson contact terms in massive electroweak theory automatically arise after recursive construction, independent of UV completion, and they automatically cancel the terms growing as (energy)$^4$ at high energy. We explore UV completion of the electroweak theory that cancels the remaining (energy)$^2$ terms and impose unitarity requirements to constrain additional couplings. The ALT shift framework allows consistent treatment in dealing with contact term ambiguities for renormalizable massive and massless theories, which we show can be useful in studying real-world amplitudes with massive spinors.

We consider a Bubble Expansion mechanism for the production of scalar dark matter during a first-order phase transition in the early Universe. Seeking for a dark matter energy density in agreement with observations, we study different non-renormalizable interactions between the dark matter species and the field undergoing the transition. The resulting relic abundance is shown to display a strong dependence on the Lorentz boost factor associated to the bubble wall motion, with this dependence becoming more significant the higher the dimension of the non-renormalizable interaction. This allows for observational compatibility across a wide range of dark matter masses and transition temperatures, typically excluded in renormalizable scenarios. For a transition around the electroweak scale, the associated gravitational wave spectrum is also within the reach of future detectors.

The Bell-CHSH inequality in the vacuum state of a relativistic scalar quantum field is revisited by making use of the Hilbert space ${\cal H} \otimes {\cal H}_{AB}$, where ${\cal H}$ and ${\cal H}_{AB}$ stand, respectively, for the Hilbert space of the scalar field and of a generic bipartite quantum mechanical system. The construction of Hermitian, field-dependent, dichotomic operators is devised as well as the Bell-CHSH inequality. Working out the $AB$ part of the inequality, the resulting Bell-CHSH correlation function for the quantum field naturally emerges from unitary Weyl operators. Furthermore, introducing a Jaynes-Cummings type Hamiltonian accounting for the interaction between the scalar field and a pair of qubits, the quantum corrections to the Bell-CHSH inequality in the vacuum state of the scalar field are evaluated till the second order in perturbation theory.

In this paper, employing the exponential corrected entropy (Chatterjee and Ghosh in Phys Rev Lett 125:041302, 2020), we derive the modified Friedmann equations from the first law of thermodynamics at apparent horizon and Verlinde's entropic gravity scenario. First, we derive the modified Friedmann equations from the first law of thermodynamics. We investigate the validity of generalised second law (GSL) of thermodynamics and find that it is always satisfied for the all eras of universe. Moreover, we investigate the deceleration parameter for the case $k=0$ in two frameworks. Finally, we numerically study the bouncing behaviour for the modified Friedmann equations obtained from entropic gravity. The results indicate that the bouncing behaviour is possible for the cases $k=1$ and $k=-1$.

We analyze boundary spin correlation functions of the hyperbolic-lattice Ising model from the holographic point of view. Using the corner-transfer-matrix renormalization group (CTMRG) method, we demonstrate that the boundary correlation function exhibits power-law decay with quasi-periodic oscillation, while the bulk correlation function always decays exponentially. On the basis of the geometric relation between the bulk correlation path and distance along the outer edge boundary, we find that scaling dimensions for the boundary correlation function can be well explained by the combination of the bulk correlation length and background curvatures inherent to the hyperbolic lattice. We also investigate the cutoff effect of the bond dimension in CTMRG, revealing that the long-distance behavior of the boundary spin correlation is accurately described even with a small bond dimension. In contrast, the sort-distance behavior rapidly loses its accuracy.

Recently, the experimental values of the muon $(g-2)_\mu$ and of the $W$ boson mass $m_{_W}$ have both indicated significant deviations from the SM predictions, motivating the exploration of extensions with extra particles and symmetries. We revisit a lepton portal model with $U(1)'$ gauge symmetry where an extra Higgs doublet, a scalar singlet and one $SU(2)_L$ singlet vector-like fermion are introduced. In this model, $(g-2)_\mu$ can be explained by extra one-loop contributions from the vector-like lepton and the $Z'$ boson, whereas $m_{_W}$ can be increased by a tree-level mixing between the $Z$ and $Z'$. Setting the $Z'$ and lepton couplings at low energies to account for the SM anomalies, we perform a Renormalization Group analysis to investigate on the high-energy behaviour of the model, in particular on the issue of vacuum stability. We find that in the alignment limit for the two Higgs doublets, the Landau pole and the scale where perturbativity is lost are of order $10-100\,{\rm TeV}$, not far from the scales experimentally reached so far, and sensibly lower than the stability scale. We show how the Landau pole can be increased up to $\sim10^9\,{\rm GeV}$ in a misaligned scenario where the experimental anomalies are still accommodated and a positive shift of the Higgs quartic coupling to improve stability can be achieved.

This article delves into the observational signatures and theoretical underpinnings of rotating astrophysical objects, with a particular focus on superspinars -exotic objects characterized by preventing the formation of event horizons due to their high angular momentum. While solutions within General Relativity (Kerr superspinars) predict such objects, their classical forms harbor naked singularities, violate causality, and exhibit problematic repulsive gravitational effects. These characteristics render classical superspinars theoretically objectionable, leading to the consideration of them as physically implausible. On the other hand, the incompatibility between General Relativity and Quantum Mechanics suggests the exploration of alternative models, particularly those in which Quantum Gravity dominates the core, yielding regular superspinars. This work demonstrates that regular superspinars avoid all the complications associated with Kerr superspinars. From a phenomenological standpoint, it is shown that the silhouettes of regular superspinars are markedly distinct from those of black holes and classical Kerr superspinars. To substantiate these differences, we perform a comprehensive analysis of inner null geodesics and investigate the structure of the Planckian region within regular superspinars. Our study reveals that only regular superspinars provide the potential for distant observers to directly observe the extremely high curvature regions within their interiors.

We investigate gravitational waves generated in $f(Q,B)$ non-metric gravity, i.e., a theory of gravity described by a non-metric compatible connection, free of torsion and curvature. It is an extension of symmetric teleparallel gravity, equipped with a boundary term $B$. This theory exhibits gravitational waves regardless of the gauge adopted: they are the standard massless tensors plus a massive scalar gravitational wave like in the case of $f(R)$ gravity. It is precisely the boundary term $B$ that generates the massive scalar mode with an effective mass $m_{B}$ associated to a Klein-Gordon equation in the linearized boundary term. As in $f(Q)$ gravity also in $f(Q,B)$ non-metric gravity, a free test particle follows a geodesic motion due to the covariant conservation with respect to the Levi-Civita connection of the energy and momentum densities on shell. Therefore, in $f(Q,B)$ gravity, the proper acceleration between two neighboring worldlines traveled by two free point-like particle is governed by a first-order geodesic deviation equation in the metric perturbation $h_{\mu\nu}$. Thanks to this approximate linear equation, $f(Q,B)$ non-metric gravity shows three polarization modes: two massless transverse tensor radiation modes, with helicity equal to 2, reproducing the standard plus and cross modes, exactly as in General Relativity, and an additional massive scalar wave mode with transverse polarization of zero helicity. We obtain the same result both by considering the coincidence gauge and by leaving the gauge free. In summary, three degrees of freedom propagate in the $f(Q,B)$ linearized theory with amplitudes $\tilde{h}^{(+)}$ and $\tilde{h}^{(\times)}$ for tensor modes and amplitude $\tilde{h}^{(s)}$ for the scalar mode. Specifically, both $f(Q,B)$ and $f(R)$ gravity involve the same massive transverse scalar perturbation.

The criterion for existence of gravitational radiation at conformal infinity in the presence of a positive cosmological constant is applied to a general family of exact solutions representing generic (pairs of) black holes of algebraic type D. Our analysis shows that only accelerating black holes generate gravitational radiation measurable at infinity. This very satisfactory result confirms the goodness of the criterion. To that end, a new metric form of the family of exact type D black holes is constructed -- including any cosmological constant and a (double-aligned) non-null electromagnetic field -- whose expression is suitable for investigation of the asymptotic structure of this large family of spacetimes. The family depends on seven physical parameters, namely $m$, $a$, $l$, $\alpha$, $e$, $g$, and $\Lambda$ that characterize mass, specific angular momentum parameter, NUT parameter, acceleration, electric and magnetic charges, and the cosmological constant, respectively.

A geometric definition of news tensor on null hypersurfaces in four space-time dimensions is presented. When the conformal Einstein field equations hold, this news tensor yields the correct expression for the radiative components of the rescaled Weyl tensor at infinity with vanishing cosmological constant in arbitrary conformal gauge. Also, a generalised transport equation for the Geroch tensor is derived. Important differences between null hypersurfaces in the bulk of the space-time and null infinity with vanishing cosmological constant are reviewed, and their impact on the role of the news is discussed.

We investigate the possibility that primordial black holes (PBHs) can be formed from large curvature perturbations generated during the waterfall phase transition in a supersymmetric scenario where sneutrino is the inflaton in a hybrid inflationary framework. We obtain a spectral index ($n_s \simeq 0.966$), and a tensor-to-scalar ratio ($r\simeq 0.0056-10^{-11}$), consistent with the current Planck data satisfying PBH as dark matter (DM) and detectable Gravitational Wave (GW) signal. Our findings show that the mass of PBH and the peak in the GW spectrum is correlated with the right-handed (s)neutrino mass. We identify parameter space where PBHs can be the entire DM candidate of the universe (with mass $10^{-13}\, M_\odot$) or a fraction of it. This could be tested via second-order GW signals in future observatories, for instance, with amplitude $\Omega_{\rm GW}h^2$ $\sim 10^{-9}$ and peak frequency $f\sim 0.1$ Hz in LISA and $\Omega_{\rm GW}h^2 \sim 10^{-11}$ and peak frequency of $\sim 10$ Hz in ET. %. for sneutrino mass $m_{\phi} \sim 2\times 10^{12}$ GeV, $\beta \sim 5.4\times 10^{15}$ GeV. We study two models of sneutrino inflation: Model$-1$ involves canonical sneutrino kinetic term which predicts the sub-Planckian mass parameter $M$, while the coupling between a gauge singlet and the waterfall field, $\beta$, needs to be quite large whereas, for the model$-2$ involving $\alpha-$attractor canonical sneutrino kinetic term, $\beta$ can take a natural value. Estimating explicitly, we show that both models have mild fine-tuning. We also derive an analytical expression for the power spectrum in terms of the microphysics parameters of the model like (s)neutrino mass, etc. that fits well with the numerical results. The typical reheat temperature for both the models is around $10^{7}-10^{8}$~GeV suitable for non-thermal leptogenesis.

We bring the Kerr--Newman spacetime into the Bondi--Sachs gauge by means of zero angular momentum, null geodesics. We compute the memory effect produced at the black hole horizon by a transient gravitational shock wave, which from future null infinity is seen as a Bondi-Metzner-Sachs supertranslation. This results in a change of the supertransformation charges at infinity between the spacetime geometries defined by the black hole before, and after, the shockwave scattering. For an extremal Kerr--Newman black hole, we give the complementary description of this process in the near-horizon limit, as seen by an observer hovering over the horizon. In this limit, we compute the supertranformation charges and compare them to those calculated at null infinity. We analyze the effect of these transformations on the electromagnetic gauge field and explore the self-interaction between this and the angular momentum of the black hole.

In this work, we provide a thorough analysis of energy extraction via magnetic reconnection, a novel mechanism recently proposed by Comisso and Asenjo, for a Kerr-Newman black hole immersed in a perfect fluid dark matter (PFDM) background. Our studies focus on the impact of black hole spin $a$, electric charge $Q$ and PFDM parameter $\lambda$ on the horizons, ecoregions and circular geodesics at the equatorial plane of this black hole, and how they further influence the reconnection efficiency and energy extraction rate. Our results show that the size of ergoregion does not vary monotonically with increasing dark matter parameters $\lambda$, but it can significantly increase at faster spins ($a>0.8$) as the dark matter parameter $\lambda$ decreases, given the electric charge stays within $Q\in [0.2,0.5]$. We identify the optimal conditions for the combination of $a$, $Q$ and $\lambda$ that enable efficient energy extraction even when the black hole is not rapidly spinning. The Kerr-Newman black hole in PFDM allows for achieving high energy extraction rates comparable to those of most previously studied rotating black holes, which typically require near-extremal spin to reach similar efficiency levels.

We have calculated the one-loop scattering amplitude of an electron by an external Coulomb potential in QED free of infrared divergences. This feature is achieved by applying the Faddeev-Kulish formalism, which implies a redefinition of both the asymptotic electronic states and of the $S$ matrix. Additionally, we have also derived the infrared-finite one-loop partial-wave amplitudes for this process by applying a recent method in the literature. Next, these partial-wave amplitudes are unitarized based on analyticity and unitarity by employing three different methods of unitarization: the algebraic $N/D$ method, the Inverse Amplitude Method and the first iterated $N/D$ method. Then, we have studied several partial waves both for physical momentum and for complex ones to look for bound-state poles. The binding momentum for the fundamental bound state in $S$ wave is discussed with special detail. This is a wide-ranging method for calculating nonperturbative partial-wave amplitudes for infinite-range interactions that could be applied to many other systems.

The critical behavior of three-state statistical models invariant under the full symmetry group $S_3$ and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order, without a definitive proof of absence of scale invariance in three-dimensional field theory with $S_3$ symmetry. This scale invariance should appear as a non-trivial fixed point of the renormalization group, which has not been found. Our new search, with the non-perturbative renormalization group, finds such a fixed point, as a bifurcation from the trivial fixed point at the critical space dimension $d=10/3$, which extends continuously to $d=3$. It does not correspond to a second-order phase transition of the 3-state Potts model, but is interesting in its own right. In particular, it shows how the $\varepsilon$-expansion can fail.

In recent studies of many-body localization in nonintegrable quantum systems, the distribution of the ratio of two consecutive energy level spacings, $r_n=(E_{n+1}-E_n)/(E_{n}-E_{n-1})$ or $\tilde{r}_n=\min(r_n,r_n^{-1})$, has been used as a measure to quantify the chaoticity, alternative to the more conventional distribution of the level spacings, $s_n=\bar{\rho}(E_n)(E_{n+1}-E_n)$, as the former unnecessitates the unfolding required for the latter. Based on our previous work on the Tracy-Widom approach to the Janossy densities, we present analytic expressions for the joint probability distribution of two consecutive eigenvalue spacings and the distribution of their ratio for the Gaussian unitary ensemble (GUE) of random Hermitian $N\times N$ matrices at $N\to\infty$, in terms of a system of differential equations. As a showcase of efficacy of our results for characterizing an approach to quantum chaoticity, we contrast them to arguably the most ideal of all quantum-chaotic spectra: the zeroes of the Riemann $\zeta$ function on the critical line at increasing heights.