Parisi-Sourlas (PS) supersymmetry is known to emerge in some models with random field type of disorder. When PS SUSY is present the $d$-dimensional theory allows for a $d-2$-dimensional description. In this paper we investigate the reversed question and we provide new indications that any given CFT$_{d-2}$ can be uplifted to a PS SUSY CFT$_{d}$. We show that any scalar four-point function of a CFT$_{d-2}$ is mapped to a set of 43 four-point functions of the uplifted CFT$_{d}$ which are related to each other by SUSY and satisfy all necessary bootstrap axioms. As a byproduct we find 43 non trivial relations between conformal blocks across dimensions. We test the uplift in generalized free field theory (GFF) and find that PS SUSY is a powerful tool to bootstrap an infinite class of previously unknown GFF observables. Some of this power is shown to persist in perturbation theory around GFF. We explain why all diagonal minimal models admit an uplift and we show exact results for correlators and CFT data of the $4d$ uplift of the Ising model. Despite being strongly coupled $4d$ CFTs, the uplifted minimal models contain infinitely many conserved currents and are expected to be integrable.

Chiral higher-spin gravity is a higher-spin extension of both self-dual Yang-Mills and self-dual gravity and is a unique local higher-spin gravity in four dimensions. Its existence implies that there are two closed subsectors in Chern-Simons matter theories. We make first steps in identifying these (anti-)chiral subsectors directly on the CFT side, which should result in a holographically dual pair where both sides are nontrivial, complete, yet exactly soluble. We also discuss closely related theories: self-dual Yang-Mills (SDYM) and self-dual gravity (SDGR) in the holographic context.

Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-spin fields. We will see here that, at linear level in these fields, the Finsler version of the Ricci tensor leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling. Nonlinear terms can also be systematically analyzed, suggesting a possible interacting structure. No particular choice of spacetime dimension is needed. The Stueckelberg mechanism breaks gauge transformations to a redundancy that does not change the geometry. This is however not enough to eliminate non-transverse modes, at least for some versions of Finsler dynamics.

Recently Danielson, Satishchandran, and Wald (DSW) have shown that quantum superpositions held outside of Killing horizons will decohere at a steady rate. This occurs because of the inevitable radiation of soft photons (gravitons), which imprint a electromagnetic (gravitational) ``which-path'' memory onto the horizon. Rather than appealing to this global description, an experimenter ought to also have a local description for the cause of decoherence. One might intuitively guess that this is just the bombardment of Hawking/Unruh radiation on the system, however simple calculations challenge this idea -- the same superposition held in a finite temperature inertial laboratory does not decohere at the DSW rate. In this work we provide a local description of the decoherence by mapping the DSW set-up onto a worldline-localized model resembling an Unruh-DeWitt particle detector. We present an interpretation in terms of random local forces which do not sufficiently self-average over long times. Using the Rindler horizon as a concrete example we clarify the crucial role of temperature, and show that the Unruh effect is the only quantum mechanical effect underlying these random forces. A general lesson is that for an environment which induces Ohmic friction on the central system (as one gets from the classical Abraham-Lorentz-Dirac force, in an accelerating frame) the fluctuation-dissipation theorem implies that when this environment is at finite temperature it will cause steady decoherence on the central system. Our results agree with DSW and provide the complementary local perspective.

We investigate the 3-sphere partition functions of various 3d $\mathcal{N}=2$ holographic SCFTs arising from the $N$ stack of M2-branes in the 't Hooft limit both analytically and numerically. We first employ a saddle point approximation to evaluate the free energy $F=-\log Z$ at the planar level, tracking the first subleading corrections in the large 't Hooft coupling $\lambda$ expansion. Subsequently, we improve these results by determining the planar free energy to all orders in the large $\lambda$ expansion via numerical analysis. Remarkably, the resulting planar free energies turn out to take a universal form, supporting a prediction that these $S^3$ partition functions are all given in terms of an Airy function even beyond the special cases where the Airy formulae were derived analytically in the literature; in this context we also present new Airy conjectures in several examples. The subleading behaviors we captured encode a part of quantum corrections to the M-theory path integrals around dual asymptotically Euclidean AdS$_4$ backgrounds with the corresponding internal manifolds through holographic duality.

We derive the generalized second law (GSL) for arbitrary cuts of Killing horizons from the perspective of crossed-product gravitational algebras, making use of a recent proposal by one of us for the construction of local gravitational algebras. This construction relies on the existence of a state whose modular flow is geometric on the horizon. In both free and interacting quantum field theories, such states are guaranteed to exist by the properties of half-sided translations on the horizon. Using geometric identities derived from the canonical analysis of general relativity on null surfaces, we show that the crossed product entropy agrees with the generalized entropy of the horizon cut in a semiclassical limit, and further reproduce Wall's result relating the GSL to monotonicity of relative entropy of the quantum field algebras. We also give a novel generalization of the GSL for interacting theories in asymptotically flat spacetimes involving the concept of an algebra at infinity for a half-sided translation, which accounts for triviality of the algebra of fields smeared only on the horizon. Going beyond the semiclassical limit, we compute subleading corrections to the crossed product entropy, but are unable to determine if the GSL continues to hold after accounting for these. We speculate that an improved GSL could follow from a hidden subalgebra structure of the crossed products, assuming the existence of an operator-valued weight between horizon cut algebras.

We study the notion of a metric over the space of AdS solution in string theory, leading to an associated distance between them. Such a distance is the idea underlying the AdS distance conjecture. We utilise the previously developed prescription for extracting such a metric: taking an off-shell quadratic variation of the string theory effective action and then evaluating it over the space of on-shell solutions. It was shown that this prescription leads to a well-defined positive metric over M-theory Freud-Rubin vacua. In this work, we use the same prescription to calculate the metric over type IIA DGKT vacua. These are much more involved, they have multiple flux parameters and exhibit scale separation. While it remains an open question whether these vacua exist as fully localised solutions of string theory, they are well-defined within the four-dimensional effective theory, which is all that is required for the calculation. We find that they also have a positive metric over them. Interestingly, this metric turns out to be independent of the many flux parameters in the solution, similarly to what happens for metrics over scalar field spaces. This non-trivial flux cancellation, as well as results from explicit vacua, lead us to propose a Swampland condition: that the metric over the space of vacua in quantum gravity, as defined by the above prescription, is always positive.

Using an exact holographic duality formula between the inhomogeneous 2d Ising model and 3d quantum gravity, we provide a formula for "real" zeroes of the 2d Ising partition function on finite graphs in terms of the geometry of a 2d triangulation embedded in the three-dimensional Euclidean space. The complex phase of those zeroes is given by the dihedral angles of the triangulation, which reflect its extrinsic curvature within the ambient 3d space, while the modulus is given by the angles within the 2d triangles, thus encoding the intrinsic geometry of the triangulation. Our formula can not cover the whole set of Ising zeroes, but we conjecture that a suitable complexification of these "real" zeroes would provide a more thorough formula. Nevertheless, in the thermodynamic limit, in the case of flat planar 2d triangulations, our Ising zeroes formula gives the critical couplings for isoradial graphs, confirming its generality. This approach shows an intricate, but precise, new relation between statistical mechanics and quantum geometry.

In the AdS$_3$/CFT$_2$ framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/$T\bar{T}$-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system's dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

We derive the cutoff length scale of the quadratic gravity in $d \geq 5$ dimensional spacetime by demanding that the quantum focusing conjecture for the smeared quantum expansion holds at the classical level. The cutoff scale has different dependence on the spacetime dimension depending on the sign of the coupling constant of the quadratic gravity. We also investigate a concrete example of the 5-dimensional Schwarzschild spacetime and directly confirm that the quantum focusing conjecture holds when the quantum expansion is smeared over the scale larger than our cutoff scale.

We study classical localised configurations - solitons - in a theory of self-interacting complex Proca field with the global $U(1)$ symmetry. We focus on spherically-symmetric solitons near the nonrelativistic limit, which are supported by the quartic interactions of the neutral Proca field. Such solitons can source the radial electric (magnetic) field if one introduces a parity-even (parity-odd) coupling of the Proca field to the electromagnetic field tensor. We discuss the conditions of existence of such nontopological ''electromagnetic hedgehogs'' and their properties.

In this work, we systematically investigate the inflationary complexity of the two-mode squeezed state with thermal effect for the single field inflation, modified dispersion relation, and non-trivial sound speed with the method of closed system and open system, respectively, which our analysis is valid for most inflationary models. First, the numeric of Krylov complexity in the method of the closed system indicates that the evolution of Krylov complexity highly depends on the squeezed angle parameter once taking the thermal effect into account, which will decay into some very tiny values, but the Krylov complexity will always enhance without thermal effect. For comparison, the numeric of circuit complexity shows that the evolution is always increasing no matter whether there are thermal effects or not which is independent of the evolution of squeezed angle parameter. By utilizing the method of open system, we first construct the wave function. As for the Krylov complexity with the method of open system, our investigations show the evolution of Krylov complexity will enhance upon some peaks factoring in the thermal effects. For completeness, we also calculate the Krylov entropy in the method of closed system and open system, which indicates that the hotter universe, the more chaotic the universe. Furthermore, our derivation for the Krylov complexity and Krylov entropy could nicely recover into the case of closed system under weak dissipative approximation, which confirms the validity of construction for the wave function. Finally, our numeric of Lanczos coefficient shows that the non-trivial sound speed has minimal chaos compared to the other two cases.

Effective Lifshitz black holes with arbitrary dynamical exponent are addressed in the fluid/gravity membrane paradigm. The transport and the response coefficients in the dual Lifshitz field theory are calculated and analyzed, including the charge diffusion constant and the shear mode damping constant, along with the shear-viscosity-to-entropy density ratio. The Kubo formula is employed to obtain the electrical DC conductivity for the gauge sector corresponding to impurity through the holographic linear response of gauge vector fluctuations in the Lifshitz black brane geometry.

We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the BMS symmetry algebra without any 2-cocycle nor central extension, at any cut of future null infinity. We refine the covariance prescription for application to the charge aspects, and introduce a new aspect for Geroch's super-momentum with better covariance properties. For the extended BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas symplectic potential exists, if one is willing to modify the symplectic structure by a corner term. The resulting algebra of Noether currents between two arbitrary cuts is center-less. The charge algebra at a given cut has a residual field-dependent 2-cocycle, but time-independent and non-radiative. More precisely, super-rotation fluxes act covariantly, but super-rotation charges act covariantly only on global translations. The take home message is that in any situation where 2-cocycles appears in the literature, covariance has likely been lost in the charge prescription, and that the criterium of covariance is a powerful one to reduce ambiguities in the charges, and can be used also for ambiguities in the charge aspects.

In this paper, we have studied the effects of pole dark energy on the evolution of gravitational waves. The background evolution of gravitational waves in a flat FRW universe is considered and its dynamics are studied in the presence of pole dark energy. Two different potential functions are considered for the study. Using the field equations, we formulated the perturbed equations governing the evolution of gravitational waves with respect to redshift z within the background of the FRW Universe. Subsequently, we delved into the characteristics of gravitational waves for the pole dark energy model and reached interesting results.

We develop a Schwinger-Keldysh field theory (SKFT) for open quantum systems interacting with a dissipative environment and apply it to the spin-boson model as an archetypical example where the environment is composed of a bosonic bath. Prior SKFT developments of this type have been confined to the Markovian regime, as an alternative to a conventional description by the Lindblad quantum master equation (QME) which is a time-local matrix differential equation. Here we combine SKFT with a two-particle irreducible (2PI) action that resums a class of Feynman diagrams to infinite order. We obtain the time-evolution of the spin density matrix in the form of a system of integro-differential equations applicable to both Markovian and non-Markovian regimes. The latter regime--where taking into account memory effects becomes essential--poses a challenge for standard methods when trying to incorporate arbitrary properties of the system, bath, and length of time evolution. The SKFT+2PI-computed time evolution of the spin expectation values in the Markovian regime reproduces the solution of the Lindblad QME, as long as the system-bath coupling in the latter is adjusted by increasing it. In the non-Markovian regime, SKFT+2PI yields a nonperturbative solution that mimics results from both hierarchical equations of motion and tensor networks methods that we employ as benchmarks. Our SKFT+2PI approach can also access challenging cases, such as zero-temperature and sub-Ohmic bath, as well as arbitrary long evolution times. Taking into account favorable numerical cost of solving the integro-differential equations with increasing number of spins, time steps or dimensionality the SKFT+2PI approach offers a promising route for simulation of driven-dissipative systems in quantum computing or quantum magnonics and spintronics in the presence of a variety of (single or multiple) dissipative environments.

The baryon acoustic oscillation (BAO) analysis from the first year of data from the Dark Energy Spectroscopic Instrument (DESI), when combined with data from the cosmic microwave background (CMB), has placed an upper-limit on the sum of neutrino masses, $\sum m_\nu < 70$ meV (95%). In addition to excluding the minimum sum associated with the inverted hierarchy, the posterior is peaked at $\sum m_\nu = 0$ and is close to excluding even the minumum sum, 58 meV at 2$\sigma$. In this paper, we explore the implications of this data for cosmology and particle physics. The sum of neutrino mass is determined in cosmology from the suppression of clustering in the late universe. Allowing the clustering to be enhanced, we extended the DESI analysis to $\sum m_\nu < 0$ and find $\sum m_\nu = - 160 \pm 90$ meV (68%), and that the suppression of power from the minimum sum of neutrino masses is excluded at 99% confidence. We show this preference for negative masses makes it challenging to explain the result by a shift of cosmic parameters, such as the optical depth or matter density. We then show how a result of $\sum m_\nu =0$ could arise from new physics in the neutrino sector, including decay, cooling, and/or time-dependent masses. These models are consistent with current observations but imply new physics that is accessible in a wide range of experiments. In addition, we discuss how an apparent signal with $\sum m_\nu < 0$ can arise from new long range forces in the dark sector or from a primordial trispectrum that resembles the signal of CMB lensing.

We consider the Euclidean vacuum for linearized gravity on the global de Sitter space, obtained from the Euclidean Green's function on the 4-sphere. We use the notion of Calder\'on projectors to recover a quantum state for the Lorentzian theory on de Sitter space. We show that while the state is gauge invariant and Hadamard, it is not positive on the whole of the phase space. We show however that a suitable modification at low energies yields a well-defined Hadamard state on global de Sitter space.

Modular flavor symmetries refers to scenarios in which fermion masses respect modular symmetries. Such scenarios have been studied in the bottom-up approach and have an explicit realization in string theory. They rely on the remarkable properties of vector-valued modular forms.

In this paper, we investigate the gravitational collapse to form the black hole in the acceleratingly expanding universe in the frame of Einstein--Gauss-Bonnet theory having two scalar fields and we study the propagation of the gravitational wave (GW). The collapsing spacetime can be obtained by using the formulation of the ``reconstruction'', that is, we find a model that realises the desired or given geometry. In the reconstructed models, ghosts often appear, which could be eliminated by imposing constraints. We show that the standard cosmological solutions or self-gravitating objects such as a planet, the Sun, various types of stars, etc., in Einstein's gravity, are also solutions in this model. Using the dynamical value of Gauss-Bonnet coupling, the propagation of the high-frequency GW is investigated. The propagating speed changes due to the coupling during the period of the black hole formation. The speed at which the GW propagates The speed at which the GW propagates going into the black hole is different from that of the wave going out.

We develop a procedure for re-summing the large logarithms induced in gravity by loops of inflationary scalars. We first show how the scalar can be integrated out of the field equations in the presence of constant graviton field. We then extend this result to a fully conserved form which explains the need for a finite renormalization of the cosmological constant which was previously inferred from explicit computation. A variant of the renormalization group turns out to explain the large logarithmic corrections revealed by explicit computation in the electric field strength of gravitational radiation and in the potentials which characterize the response to a point mass. The implications for graviton loops are discussed.

We study in detail the influence of different chemical potentials (baryon, charged, strange, and neutrino) on how and how fast a free gas of quarks in the zero-temperature limit reaches the conformal limit. We discuss the influence of non-zero masses, the inclusion of leptons, and different constraints, such as charge neutrality, zero-net strangeness, and fixed lepton fraction. We also investigate for the first time how the symmetry energy of the system under some of these conditions approaches the conformal limit. Finally, we briefly discuss what kind of corrections are expected from perturbative QCD as one goes away from the conformal limit.

The canonical quantisation of General Relativity including matter on a spacetime manifold in the globally hyperbolic setting involves in particular the representation theory of the spatial diffeomorphism group (SDG), and/or its Lie algebra (SDA), of the underlying spatial submanifold. There are well known Fock representations of the SDA in one spatial dimension and non-Fock representations of the SDG in all dimensions. The latter are not strongly continuous and do not descend to representations of the SDA. In this work we report some partial results on non anomalous representations of the SDA for both geometry and matter: 1. Background independent Fock representations of the SDA by operators exist in all dimensions. 2. Infinitely many unitary equivalence classes of background dependent Fock representations of the SDA by operators exist in one dimension but these do not extend to higher dimensions. 3. Infinitely many unitary equivalence classes of background dependent Fock representations of the SDA of volume preserving diffeomorphisms by operators exist in all dimensions. 4. Infinitely many unitary equivalence classes of background dependent Fock representations of the SDA by quadratic forms exist in all dimensions. Except for 1. these representations do not descend from an invariant state of the Weyl algebra and 4. points to a new strategy for solving the quantum constraints.

Perturbative quantum gravity starts from prescribing a background metric. That background metric is then used in order to carry out two separate steps: 1. One splits the non-perturbative metric into background and deviation from it (graviton) and expands the action in terms of the graviton which results in an ifinite series of unknown radius of convergence. 2. One constructs a Fock representation for the graviton and performs perturbative graviton quantum field theory on the fixed background as dictated by the perturbative action. The result is a non-renormalisable theory without predictive power. It is therefore widely believed that a non-perturbative approach is mandatory in order to construct a fundamental, not only effective, predictive quantum field theory of the gravitational interaction. Since perturbation theory is by definition background dependent, the notions of background dependence (BD) and perturbation theory (PT) are often considered as symbiotic, as if they imply each other. In the present work we point out that there is no such symbiosis, these two notions are in fact logically independent. In particular, one can use BD structures while while not using PT at all. Specifically, we construct BD Fock representations (step 2 above) for the full, non-perturbative metric rather than the graviton (not step 1 above) and therefore never perform a perturbative expansion. Despite the fact that the gravitational Lagrangean is a non-polynomial, not even analytic, function of the metric we show that e.g. the Hamiltonian constraint with any density weight can be defined as a quadratic form with dense form domain in such a representation.

This work investigates the intricate relationship between the q-boson model, a quantum integrable system, and classical integrable systems such as the Toda and KP hierarchies. Initially, we analyze scalar products of off-shell Bethe states and explore their connections to tau functions of integrable hierarchies. Furthermore, we discuss correlation functions within this formalism, examining their representations in terms of tau functions, as well as their Schur polynomial expansions.

This thesis is developed in the context of the spin-foam approach to quantum gravity; all results are concerned with the Lorentzian theory and with semiclassical methods. A correspondence is given between Majorana 2-spinors and time-like hypersurfaces in Minkowski 3-space based on complexified quaternions. It is shown that the former suggest a symplectic structure on the spinor phase space which, together with an area-matching constraint, yields a symplectomorphism to $T^*\mathrm{SU}(1,1)$. A complete 3-dimensional Lorentzian spin-foam amplitude for both space- and time-like triangles is proposed. It is shown to asymptote to Regge theory in the semiclassical regime. The asymptotic limit of the 4-dimensional Conrady-Hnybida model for general polytopes is scrutinized. Minkowski's theorem on convex polyhedra is generalized to Lorentzian signature, and new boundary states for time-like polygons are introduced. It is found that the semiclassical amplitude for such polygons is insufficiently constrained. A method for the asymptotic evaluation of integrals subject to external parameters is discussed. The method is developed in detail for the special problem of spin-foam gluing constraints away from their dominant critical points. A relation to the gluing constraints of effective spin-foams is suggested.

Different approaches to quantum gravity, such as loop quantum cosmology and group field theory, predict the resolution of the initial cosmological singularity via a 'bounce': a regular spacetime region that connects the expanding branch of the universe to a contracting branch. The cosmological arrow of time, which by definition points in the direction of cosmic expansion, is reversed at the bounce. Nonetheless, it is still possible to discriminate between the two branches by considering different arrows, as defined for instance by the growth of perturbations. After reviewing general aspects of the time arrow problem in cosmology, we examine the properties of different arrows of time in bouncing cosmologies, focusing on the loop quantum cosmology bounce as a case study. We also present a new exact solution to the effective Friedmann equations of loop quantum cosmology with pressureless dust and a cosmological constant, which is a simplified version of the $\Lambda$CDM bounce scenario, where these issues can be examined in detail.

The Gertsenshtein effect could in principle be used to detect a single graviton by firing it through a region filled with a constant magnetic field that enables its conversion to a photon, which can be efficiently detected via standard techniques. The quantization of the gravitational field could then be inferred indirectly. We show that for currently available single-photon detector technology, the Gertsenshtein detector is generically inefficient, meaning that the probability of detection is $\ll 1$. The Gertsenshtein detector can become efficient on astrophysical scales for futuristic single-photon detectors sensitive to frequencies in the Hz to kHz range. It is not clear whether such devices are in principle possible.

We expound upon our (polarization-free) definition of the quantization map in geometric quantization, which is justified using the Poisson sigma model and pieces together most known quantization schemes. We use it to obtain the noncommutative torus and a finite dimensional irreducible representation. We discuss invariance of polarization using Schur's lemma.