### From Rotating to Charged Black Holes and Back Again

The mild form of the Weak Gravity Conjecture (WGC) requires higher derivative corrections to extremal charged black holes to increase their charge-to-mass ratio. This allows decay via emission of a smaller extremal black hole. In this paper, we investigate if similar constraints hold for extremal rotating black holes. We do so by considering the leading higher derivative corrections to the four-dimensional Kerr black hole and five-dimensional Myers-Perry black hole. We use a known mapping of these rotating solutions to a four-dimensional non-rotating dyonic Kaluza-Klein black hole and impose the WGC on this charged solution. Going back again to the rotating solutions, this fixes the sign of the corrections to the rotating extremality bounds. The sign of the corrections is non-universal, depending on the black hole under consideration. We argue that this is not at odds with black hole decay, because of the presence of a superradiant instability that persists in the extremal limit. When this instability is present, the WGC is implied for the four-dimensional charged black hole.

### A perfect fluid hydrodynamic picture of domain wall velocities at strong coupling

We show that for a range of strongly coupled theories with a first order phase transition, the domain wall or bubble velocity can be expressed in a simple way in terms of a perfect fluid hydrodynamic formula, and thus in terms of the equation of state. We test the predictions for the domain wall velocities using the gauge/gravity duality.

### Black Holes Decohere Quantum Superpositions

We show that if a massive body is put in a quantum superposition of spatially separated states, the mere presence of a black hole in the vicinity of the body will eventually destroy the coherence of the superposition. This occurs because, in effect, the gravitational field of the body radiates soft gravitons into the black hole, allowing the black hole to acquire "which path" information about the superposition. A similar effect occurs for quantum superpositions of electrically charged bodies. We provide estimates of the decoherence time for such quantum superpositions. We believe that the fact that a black hole will eventually decohere any quantum superposition may be of fundamental significance for our understanding of the nature of black holes in a quantum theory of gravity.

### Higgs/Amplitude Mode Dynamics From Holography

Second order phase transitions are universally driven by an order parameter which becomes trivial at the critical point. At the same time, collective excitations which involve the amplitude of the order parameter develop a gap which smoothly closes to zero at criticality. We develop analytical techniques to study this "Higgs" mode in holographic systems which undergo a continuous phase transition at finite temperature and chemical potential. This allows us to study the linear response of the system at energy scales of the order of the gap. We express the Green's functions of scalar operators in terms of thermodynamic quantities and a single transport coefficient which we fix in terms of black hole horizon data.

### Entanglement distillation towards minimal bond cut surface in tensor networks

We propose that a minimal bond cut surface is characterized by entanglement distillation in tensor networks. Our proposal is not only consistent with the holographic models of perfect or tree tensor networks, but also can be applied for several different classes of tensor networks including matrix product states and multi-scale entanglement renormalization ansatz. We confirmed our proposal by a numerical simulation based on the random tensor network. The result sheds new light on a deeper understanding of the Ryu-Takayanagi formula for entanglement entropy in holography.

### The Natural TeV Cutoff of the Higgs Field from the Multiplicative Lagrangian

The various types of Lagrangian can be added to the standard Lagrangian with the invariant of the equation of motion. In this paper, we construct the multiplicative Lagrangian of a complex scalar field giving the Klein-Gordon equation from the inverse problem of the calculus of variation. Then, this multiplicative Lagrangian with arbitrary high cutoff is applied to the toy model of the Higgs mechanism in U(1)-gauge symmetry in order to study the simple effects in the Higgs physics. We show that, after spontaneous symmetry breaking happens, the Higgs vev is free from the Fermi-coupling constant and the Higgs field gets the natural cutoff in TeV scale. The other relevant coupling constants, the UV-sensitivity of Higgs mass due to the loop correction, some applications on the strong CP problem as well as anomalous small fermion mass, and the cosmological constant problem are also discussed.

### Background Effective Action with Nonlinear Massive Gauge Fixing

We combine a recent construction of a BRST-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background-field invariance as well as BRST invariance of the quantum field manifestly. The construction features BRST-invariant mass parameters for the quantum gauge and ghost fields. The formalism employs a background Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and thus should not affect observables. We verify this expectation by computing the one-loop effective action and the corresponding beta function of the gauge coupling as an example. The corresponding Schwinger functional generating connected correlation functions acquires additional one-particle reducible terms that vanish on shell. We also study off-shell one-loop contributions in order to explore the consequences of a nonlinear gauge fixing scheme involving a background Nakanishi-Lautrup field. As an application, we show that our formalism straightforwardly accommodates nonperturbative information about propagators in the Landau gauge in the form of the so-called decoupling solution. Using this nonperturbative input, we find evidence for the formation of a gluon condensate for sufficiently large coupling, whose scale is set by the BRST-invariant gluon mass parameter.

### Lorentz Invariance, Scattering Amplitudes and the Emergence of Semiclassical Geometry

It has been known for some time now that error correction plays a fundamental role in the determining the emergence of semiclassical geometry in quantum gravity. In this work I connect several different lines of reasoning to argue that this should indeed be the case. The kinematic data which describes the scattering of $N$ massless particles in flat spacetime can put in one-to-one correspondence with coherent states of quantum geometry. These states are labeled by points in the Grassmannian $Gr_{2,n}$, which can be viewed as labeling the code-words of a quantum error correcting code. The condition of Lorentz invariance of the background geometry can then be understood as the requirement that co-ordinate transformations should leave the code subspace unchanged. In this essay I show that the language of subsystem (or operator) quantum error correcting codes provides the proper framework for understanding these aspects of particle scattering and quantum geometry.

### Exact Geometries from Boundary Gravity

We show that the extremal Reissner-Nordstr\"{o}m type multi black holes in an emergent scenario are exact in General Relativity. It is shown that an axion in the bulk together with a geometric torsion ensure the required energy-momentum to source the $(3$$+$$1)$ geometry in the Einstein tensor. Analysis reveals a significant role of dark energy to the curved space-time.

### Electric and chiral response to pseudoelectric field in Weyl materials

The electric and chiral current response to the time and coordinate dependent pseudoelectric field $\mathbf{E}_5$ in Weyl semimetals is studied. It is found that $\mathbf{E}_5$ leads to an electric current in the direction perpendicular to the field and the wave vector of the perturbation. We dubbed this effect the anomalous pseudo-Hall effect. The response of the chiral or valley current to the pseudoelectric field is also found to be nontrivial. Since the wave vector for $\mathbf{E}_5$ cannot be neglected, the frequency profile of the chiral conductivity is drastically different from its electric counterpart showing a step-like feature instead of a smooth Drude peak. The proposed effects can be investigated by driving sound waves in Weyl semimetals with broken time-reversal symmetry.

### Cosmology in the presence of diffeomorphism-violating, nondynamical background fields

We consider diffeomorphism violation, which is parameterized by nondynamical background fields of the gravitational Standard-Model Extension (SME), and study its effects on the time evolution of the Universe. Our goal is to identify background field configurations that imply stages of accelerated expansion without exotic forms of matter and radiation present. Although our approach gives rise to a set of restrictive conditions, configurations are encountered that exhibit this property or show other interesting behaviors. The findings of our article, which is among the first to apply the SME to a cosmological setting, provide an initial understanding of how to technically incorporate background fields into the cosmological evolution equations and what their phenomenological impact may be.

### Master integrals for ${\cal O}(αα_s)$ corrections to $H \to ZZ^*$

We present analytic results for all the Feynman integrals relevant for ${\mathcal O}(\alpha \alpha_s)$ virtual corrections to $H \rightarrow ZZ^*$ decay. We use the method of differential equations to solve the master integrals while keeping the full dependence on the masses of all the particles including internal propagators. Due to the presence of four mass scales we encounter multiple square roots. We argue that all the occurring square roots can not be rationalized at the same time as a simultaneous rationalization brings us to integrals over $CY_3$ manifolds. Hence we rationalize only three square roots simultaneously and construct suitable ans\"atze to obtain dlog-forms containing the square root, after obtaining an epsilon-factorised form for the differential equations. We present the alphabet and the analytic form of all the boundary constants that appear in the solutions of the differential equations. The results for master integrals are expressed in terms of Chen's iterated integrals with dlog one-forms.

### Average capacity of quantum entanglement

As an alternative to entanglement entropies, the capacity of entanglement becomes a promising candidate to probe and estimate the degree of entanglement of quantum bipartite systems. In this work, we study the typical behavior of entanglement capacity over major models of random states. In particular, the exact and asymptotic formulas of average capacity have been derived under the Hilbert-Schmidt and Bures-Hall ensembles. The obtained formulas generalize some partial results of average capacity computed recently in the literature. As a key ingredient in deriving the results, we make use of recent advances in random matrix theory pertaining to the underlying orthogonal polynomials and special functions. Numerical study has been performed to illustrate the usefulness of average capacity as an entanglement indicator.

### Dynamics and entanglement in quantum and quantum-classical systems: lessons for gravity

Motivated by quantum gravity, semiclassical theory, and quantum theory on curved spacetime, we study the system of an oscillator coupled to two spin-1/2 particles. This simple model provides a prototype for comparing three types of dynamics: the full quantum theory, the classical oscillator with spin backreaction, and spins propagating on a fixed oscillator background. From nonperturbative calculations of oscillator and entanglement entropy dynamics, we find that (i) entangled tripartite states produce novel oscillator trajectories, (ii) the three systems give equivalent dynamics for sufficiently weak oscillator-spin couplings, and (iii) spins driven by a classical oscillator, with or without backreaction, can produce entangled spin states. The latter result suggests a counterpoint to claims that gravity must be quantized to produce entangled matter states.

### Angular-time evolution for the Affleck-Kennedy-Lieb-Tasaki chain and its edge-state dynamics

We study the angular-time evolution that is a parameter-time evolution defined by the entanglement Hamiltonian for the bipartitioned ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain with the open boundary. In particular, we analytically calculate angular-time spin correlation functions $\langle S_n^\alpha(\tau)S_n^\alpha(0)\rangle$ with $\alpha = x,y,z$, using the matrix-product-state (MPS) representation of the valence-bond-solid state with edges. We also investigate how the angular-time evolution operator can be represented in the physical spin space with the use of gauge transformation for the MPS. We then discuss the physical interpretation of the angular-time evolution in the AKLT chain.

### Inflation and primordial gravitational waves in scale-invariant quadratic gravity

In scale-invariant models of fundamental physics all mass scales are generated via spontaneous symmetry breaking. In this work, we study inflation in scale-invariant quadratic gravity, in which the Planck mass is generated classically by a scalar field, which evolves from an unstable fixed point to a stable one thus breaking scale-invariance. We investigate the dynamics by means of dynamical system standard techniques. By computing the spectral indices and comparing them with data, we put some constraints on the three dimensionless parameters of the theory. We show that certain regions of the parameter space will be within the range of future CMB missions like CMB-S4, LiteBIRD and STPol. The second half of the paper is dedicated to the analysis of inflationary first-order tensor perturbations and the calculation of the power spectrum of the gravitational waves. We comment on our results and compare them with the ones of mixed Starobinsky-Higgs inflation.

### Cosmological Constant and Vacuum Zero Point Energy in Black Hole Backgrounds

We study the quantum vacuum zero point energy in the Schwarzschild black hole as well as in the Nariai limit of the dS-Schwarzschild backgrounds. We show that the regularized vacuum energy density near the black hole and also in the Nariai setup match exactly with the corresponding value in the flat background, scaling with the fourth power of the mass of the quantum field. The horizon radius of the dS space created from the vacuum zero point energy introduces a new length scale which should be compared with the black hole horizon radius. There is an upper limiting mass for the black hole immersed in the vacuum zero point energy which is determined by the mass of the Nariai metric associated to the dS background constructed from zero point energy. This result supports the proposal made recently that the dS spacetime created from the vacuum zero point energy develops strong inhomogeneities on sub-horizon scales in which the regions inside the dS horizon radius may collapse to form black holes.

### Notes on the experimental observation of the Unruh effect

The incorporation of classical general relativity into quantum field theory yields a surprising result -- thermodynamic particle production. One such phenomenon, known as the Unruh effect, causes empty space to effervesce a thermal bath of particles when viewed by an observer undergoing uniformly accelerated motion. These systems will have a Rindler horizon which produces this Unruh radiation at the Fulling-Davies-Unruh temperature. For accelerated charges, the emission and absorption of this radiation will imprint the FDU temperature on photons emitted in the laboratory. Each of these photons will also change the Rindler horizon in accordance with the Bekenstein-Hawking area-entropy law. In this essay, we will discuss these aspects of acceleration-induced thermality which have been experimentally observed in a high energy channeling experiment carried out by CERN-NA63.

### The more things change the more they stay the same: Minimum lengths with unmodified uncertainty principle and dispersion relation

Broad arguments indicate that quantum gravity should have a minimal length scale. In this essay we construct a minimum length model by generalizing the time-position and energy-momentum operators while keeping much of the structure of quantum mechanics and relativity intact: the standard position-momentum commutator, the special relativistic time-position, and energy-momentum relationships all remain the same. Since the time-position and energy-momentum relationships for the modified operators remains the same, we retain a form of Lorentz symmetry. This avoids the constraints on these theories coming from lack of photon dispersion while holding the potential to address the Greisen-Zatsepin-Kuzmin (GZK) puzzle of ultra high energy cosmic rays.

### A unified field theory from a complexified quaternion-octonion Dirac equation

It is set manifest an underlying algebraic structure of Dirac equation and solutions, in terms of C$\ell_2$ Clifford algebra projectors and ladder operators. From it, a scheme is proposed for constructing unified field theories by enlarging the pointed algebra. A toy unified matter field model is formulated, modifying Dirac equation with complex quaternions and octonions. The result describes a set of fermion fields with reminiscent properties of one standard model particle generation, exhibiting U(1) electromagnetism, SU(2) flavor and SU(3) color like symmetries, remarkably SU(2) induces frame fields, though further explorations are needed.

### Chiral effects in classical spinning gas

We consider a statistical mechanics of rotating ideal gas consisting of classical non-relativistic spinning particles. The microscopic structure elements of the system are massive point particles with a nonzero proper angular momentum. The norm of proper angular momentum is determined by spin. The direction of proper angular momentum changes continuously. Applying the Gibbs canonical formalism for the rotating system, we construct the one-particle distribution function, generalising the usual Maxwell-Boltzmann distribution, and the partition function of the system. The model demonstrates a set of chiral effects caused by interaction of spin and macroscopic rotation, including the change of entropy, heat capacity, chemical potential and angular momentum.

### Spatial entanglement in two dimensional QCD: Renyi and Ryu-Takayanagi entropies

We derive a general formula for the replica partition function in the vacuum state, for a large class of interacting theories with fermions, with or without gauge fields, using the equal-time formulation on the light front. The result is used to analyze the spatial entanglement of interacting Dirac fermions in two-dimensional QCD. A particular attention is paid to the issues of infrared cut-off dependence and gauge invariance. The Renyi entropy for a single interval, is given by the rainbow dressed quark propagator to order ${\cal O}(N_c)$. The contributions to order ${\cal O}(1)$, are shown to follow from the off-diagonal and off mass-shell mesonic T-matrix, with no contribution to the central charge. The construction is then extended to mesonic states on the light front, and shown to probe the moments of the partonic PDFs for large light-front separations. In the vacuum and for small and large intervals, the spatial entanglement entropy following from the Renyi entropy, is shown to be in agreement with the Ryu-Takayanagi geometrical entropy, using a soft-wall AdS$_3$ model of two-dimensional QCD.