We explore asymptotically locally anti-de Sitter spacetimes exhibiting gravitational radiative behavior, employing null gauges that allow for a well-defined flat limit. The radiative content in the bulk is captured by the boundary Cotton and stress tensor, which we collect into a radiative vector. We reinterpret this vector holographically in terms of fluid variables in the dual boundary theory. For algebraically special solutions, we uncover a close connection between bulk radiation and dissipative corrections in the boundary stress tensor, demonstrating a direct link between radiation and entropy production in the boundary fluid. This reveals a rich interplay between radiative dynamics in the bulk and out-of-equilibrium conformal physics at the boundary. We then investigate the flat limit of this correspondence in the context of flat-space holography. In this setting, we construct a Carrollian analogue of the radiative vector and introduce Celestial observables, such as energy detectors, which emerge naturally from the bulk’s radiative structure. Our analysis shows that bulk radiation sources the Carrollian viscous stress tensor and heat current, which encodes the Bondi news in this framework. We illustrate our results with explicit examples, including Robinson-Trautman spacetimes and accelerating black holes.

We embed the covariant, gauge-invariant gravitational radiation criteria of Fernández-Álvarez and Senovilla, based on conformal geometry and the Bel–Robinson tensor, into the hydrodynamic framework of gauge/gravity duality. This construction uncovers a direct correspondence between bulk gravitational waves and dissipative processes in the boundary fluid, from which a natural notion of entropy production emerges. We further analyze a smooth flat-space limit in which the dual fluid becomes Carrollian, with dissipation governed by Carroll-covariant tensors. As an example, we apply our framework to the Robinson–Trautman family of solutions.

In the framework of AdS/CFT correspondence, the Fefferman-Graham (FG) gauge offers a useful way to express asymptotically anti-de Sitter spaces, allowing a clear identification of their boundary structure. A known feature of this approach is that choosing a particular conformal representative for the boundary metric breaks explicitly the boundary scaling symmetry. Recent developments have shown that it is possible to generalize the FG gauge to restore boundary Weyl invariance by adopting the Weyl-Fefferman-Graham gauge. In this paper, we focus on three-dimensional gravity and study the emergence of a boundary Weyl structure when considering the most general AdS boundary conditions introduced by Grumiller and Riegler [1]. We extend the holographic renormalization scheme to incorporate Weyl covariant quantities, identifying new subleading divergences appearing at the boundary. To address these, we introduce a new codimension-two counterterm, or corner term, that ensures the finiteness of the gravitational action. From here, we construct the quantum-generating functional, the holographic stress tensor, and compute the corresponding Weyl anomaly, showing that the latter is now expressed in a full Weyl covariant way. Finally, we discuss explicit applications to holographic integrable models and accelerating black holes. For the latter, we show that the new corner term plays a crucial role in the computation of the Euclidean on-shell action.

We study magnetotransport in a holographic model where ModMax nonlinear electrodynamics is coupled to Einstein AdS gravity. To incorporate momentum relaxation, we introduce spatially linear axion fields that break translational symmetry, resulting in an anisotropic medium. Using linear response theory, we compute the DC conductivity matrix in the presence of an external magnetic field, expressing the conductivities in terms of horizon data. Our results demonstrate how the nonlinear ModMax parameter modifies charge transport, particularly influencing the Hall angle and Nernst signal. The nonlinear corrections introduce distinct deviations in both longitudinal and Hall conductivities while preserving the characteristic temperature scaling of strange metals, offering new insights into strongly coupled systems with nonlinear electromagnetic interactions. Notably, the Nernst signal reproduces that of high-T_c cuprate superconductors showing a superconducting dome and a normal phase, with the ModMax deformation parameter tuning critical and onset temperatures. In the strongly nonlinear regime, we find evidence of an exotic state dominated by quasiparticle excitations in the dual material.

We study the renormalization of a particular sector of Horndeski theory. In particular, we focus on the nonminimal coupling of a scalar field to the Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a power expansion on the scalar function that couples the Gauss-Bonnet term, we find specific conditions on their coefficients such that the action and charges are finite. To accomplish the latter, we add a finite set of intrinsic boundary terms. The contribution of the nonminimal coupling generates an effective scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound. Furthermore, we compute the holographic 1-point functions and Ward identities associated with the scalar field and the metric. We constrain the parameter space of the theory by taking into account the preservation of scaling symmetry at the boundary.

This paper completes the analysis initiated in the companion work arXiv:2403.02283 — referred to as Paper I — by showing how Vasiliev’s 4D higher-spin gravity (HSG) and 3D coloured conformal matter fields coupled to conformal higher-spin gauge fields and colour gauge fields (coloured conformal HSG, or CCHSG) emerge as consistent reductions of a common parent model. The latter is a Frobenius-Chern-Simons model with superconnection valued in a fractional-spin extension of Vasiliev’s higher-spin algebra, and was defined and studied in Paper I. Here, we i) realize HSG as a subcase of a more general 4D reduction, describing HSG coupled to coloured, fractional-spin matter, which we refer to as 4D fractional-spin gravity; ii) study the CCHSG model, in particular exhibiting the crucial role played by novel colour gauge fields in coupling conformal matter to conformal HSG, thereby completing the models due to Vasiliev and Nilsson; iii) extract conformal currents and composite coloured sources in an expansion of the CCHSG model around 3D Minkowskian leaves; and iv) compare our results with Vasiliev’s holography proposal of arXiv:1203.5554. The common origin of HSG and CCHSG, besides relating the two models directly, is the starting point for establishing the holographic correspondence between the two models via overlap conditions, to be presented separately.

Entanglement entropy is crucial for understanding the link between quantum mechanics and information theory. This thesis investigates how energy fluctuations and acceleration affect entanglement entropy through three key scenarios. First, we analyze entanglement between disjoint Rindler observers in de Sitter spacetime. We introduce 1-loop corrections to the partition function of the conformal field theory, disrupting the previously flat entanglement spectrum and resulting in an area law for entanglement entropy, while preserving the finiteness of the Hilbert space. Next, we extend the holographic entanglement entropy framework to field theories with global U(1) symmetry, considering non-linearly charged theories and their thermal and quantum fluctuations. We find that the dual theory experiences spontaneous symmetry breaking and a reduction in the leading-order coefficient of the ⟨ TT⟩ correlator due to quantum corrections. Using conformal electrodynamics coupled with three-dimensional gravity as an example, we explore a black hole solution and its connection to two-dimensional free bosons. Finally, we investigate three-dimensional accelerating black holes, revealing that increased acceleration reduces the accessible boundary region and, consequently, the entanglement entropy. This suggests a loss of information in the dual theory due to acceleration.

In this work and in the companion paper arXiv:2403.02301, we initiate an approach to holography based on the AKSZ formalism. As the first step, we refine Vasiliev’s holography proposal in arXiv:1203.5554 by obtaining 4D higher-spin gravity (HSG) and 3D coloured conformal higher-spin gravity (CCHSG) — i.e., coloured conformal matter fields coupled to conformal higher-spin gauge fields and colour gauge fields — as two distinct and classically consistent reductions of a single parent theory. The latter consists, on-shell, of a flat superconnection valued in a fractional-spin extension of Vasiliev’s higher-spin algebra. The HSG and CCHSG reductions are characterized by dual structure groups and two-form cohomology elements, and their embedding in a common parent model provides a rationale for deriving holographic relations from multi-dimensional AKSZ partition functions on cylinders with dual boundary conditions, to appear separately. In this work we i) construct the underlying non-commutative geometry as a metaplectic operator algebra represented in a Hermitian module of a pair of conformal particles; ii) identify a discrete modular group, arising from twisted boundary conditions of the first-quantized system, and connecting different boundary conditions of the second-quantized system; and iii) identify the holonomies, structure groups and two-form cohomology elements that characterize the HSG and CCHSG reductions, and equate the dual second Chern classes.

This paper studies the holographic description of 2 + 1-dimensional accelerating black holes. We start by using an ADM decomposition of the coordinates suitable to identify boundary data. As a consequence, the holographic CFT lies in a fixed curved background which is described by the holographic stress tensor of a perfect fluid. We compute the Euclidean action ensuring that the variational principle is satisfied in the presence of the domain wall. This requires including the Gibbons-Hawking-York term associated with internal boundaries on top of the standard renormalised AdS3 action. Finally, we compute the entanglement entropy by firstly mapping the solution to the Rindler-AdS spacetime in which the Ryu-Takayanagi surface is easily identifiable. We found that as the acceleration increases the accessible region of the conformal boundary decreases and also the entanglement entropy, indicating a loss of information in the dual theory due to acceleration.

Abstract In the realm of lower-dimensional accelerating spacetimes, it is well-established that the presence of domain walls, which are co-dimension one topological defects, is a necessary condition for their construction. We expand upon the geometric framework employed in the generation of such spacetime solutions by incorporating a conformally coupled scalar field within the matter sector. This endeavor leads to the identification of several new families of three-dimensional accelerating spacetimes with asymptotically locally anti-de Sitter (AdS) behavior. Notably, one of these solutions showcases a hairy generalization of the accelerating BTZ black hole. This solution is constructed at both slow and rapid phases of acceleration, and its connection with established vacuum spacetime models is explicitly elucidated. The inclusion of the scalar field imparts a non-constant Ricci curvature to the domain wall, thereby rendering these configurations particularly suitable for the construction of two-dimensional quantum black holes. To establish a well-posed variational principle in the presence of the domain wall, two essential steps are undertaken. First, we extend the conventional renormalized AdS3 action to accommodate the presence of the scalar field. Second, we explicitly incorporate the Gibbons-Hawking-York term associated with the internal boundaries of our geometries and account for the tension of the domain wall in the action. This dual step process enables us to derive the domain wall field equations via the variational principle. Consequently, the action furnishes the appropriate quantum statistical relation. We engage in holographic computations, thereby determining the explicit form of the holographic stress tensor. In this context, the stress tensor can be expressed as that of a perfect fluid situated on a curved background. Additionally, it paves the road to ascertain the spacetime mass. Finally, we close by demonstrating the existence of three-dimensional accelerating spacetimes with asymptotically locally flat and asymptotically locally de Sitter geometries, particularly those embodying black holes.

We extend the charged Renyi entropy to a more general holographic scenario. Coupling an arbitrary non-linear electrodynamics Lagrangian density to AdS gravity, we analyse the thermodynamic features of non-linearly charged hyperbolic black holes and the thermal fluctuations in the grand canonical ensemble. We provide a general form for the relevant holographic quantities that describes a CFT with a global U(1) symmetry in terms of horizon data and we compute the first thermal fluctuation of the charged Renyi entropy. We demonstrate the validity of the formulae through an analytic example; the Coulomb source in 2 + 1 dimensions. We propose this model to be dual to charged free bosons in 1 + 1 dimensions. The corrections generates a subleading logarithmic divergence in the entanglement entropy which appear in some Condensed Matter systems with spontaneous symmetry breaking due to IR effects in the ground state. We comment on the possibility of interpreting these results in terms of holography beyond the saddle point approximation.

The production of heavy mass resonances has been widely studied theoretically and experimentally. Several extensions of the standard model (SM) of particle physics, naturally give rise to a new resonance, with neutral electric charge, commonly referred to as the $\textrm{Z}^{\prime}$ boson. The nature, mass, couplings, and associated quantum numbers of this hypothetical particle are yet to be determined. We present a feasibility study on the production of a vector like $\textrm{Z}^{\prime}$ boson at the LHC, with preferential couplings to third generation fermions, considering proton-proton collisions at $\sqrt{s} = 13$ $\mathrm{TeV}$ and 14 TeV. We work under two simplified phenomenological frameworks where the $\mathrm{Z}^{\prime}$ masses and couplings to the SM particles are free parameters, and consider final states of the $\textrm{Z}^{\prime}$ decaying to a pair of $\mathrm{b}$ quarks. The analysis is performed using machine learning techniques in order to maximize the experimental sensitivity. The proposed search methodology can be a key mode for discovery, complementary to the existing search strategies considered in literature, and extends the LHC sensitivity to the $\mathrm{Z}^{\prime}$ parameter space.

It has been argued that the entropy of de Sitter space corresponds to the entanglement between disconnected regions computable by switching on a replica parameter q modeled by the quotient dS/ℤq. Within this framework, we show that the centrally-extended asymptotic symmetry algebra near the cosmic horizon is a single copy of the Virasoro algebra. The resulting density of states matches the semi-classical result of Gibbons and Hawking up to an undetermined constant that is chosen to reproduce the entanglement entropy previously found in the literature. It follows that the logarithmic quantum corrections to the Cardy entropy reproduces the known one-loop result computed in the bulk in the presence of a cutoff. The resulting entanglement entropy follows the divergent area law, where the UV cutoff is now a function of the replica parameter. Thus, as the near-horizon CFT fixes the cutoff in units of the Planck scale, the model can be viewed as a probe into whether the defect Hilbert space has a finite dimension; indeed, the limit q → 0, reproduces Banks’ formula. We also study the quantum corrections of the effective description of the horizon entropy by means of Liouville field theory, where the large q limit corresponds to a realization of dS3/CFT2 correspondence matching the logarithmic corrections to three-dimensional de Sitter space obtained by computing the one-loop contribution to the quantum gravity partition function in the round three-sphere.

We model the back-reaction of a static observer in four-dimensional de Sitter spacetime by means of a singular ℤq quotient. The set of fixed points of the ℤq action consists of a pair of codimension two minimal surfaces given by 2-spheres in the Euclidean geometry. The introduction of an orbifold parameter q > 1 permits the construction of an effective action for the bulk gravity theory with support on each of these minimal surfaces. The effective action corresponds to that of Liouville field theory on a 2-sphere with a finite vacuum expectation value of the Liouville field. The intrinsic Liouville theory description yields a thermal Cardy entropy that we reintrepret as a modular free energy at temperature T = q−1, whereupon the Gibbons-Hawking entropy arises as the corresponding modular entropy. We further observe that in the limit q → ∞ the four-dimensional geometry reduces to that of global dS3 spacetime, where the two original minimal surfaces can be mapped to the future and past infinities of dS3 by means of a double Wick rotation. In this limit, the Liouville theories on the minimal surfaces become boundary theories at zero temperature whose total central charge equals that computed using the dS3/CFT2 correspondence.

We argue that the notion of entanglement in de Sitter space arises naturally from the non-trivial Lorentzian geometry of the spacetime manifold, which consists of two disconnected boundaries and a causally disconnected interior. In four bulk dimensions, we propose an holographic description of an inertial observer in terms of a thermofield double state in the tensor product of the two boundaries Hilbert spaces, whereby the Gibbons–Hawking formula arises as the holographic entanglement entropy between the past and future conformal infinities. When considering the bulk entanglement between the two causally disconnected Rindler wedges, we show that the corresponding entanglement entropy is given by one quarter of the area of the pair of codimension two minimal surfaces that define the set of fixed points of the dS orbifold.

De Sitter space, unlike its negatively curved relative, consists of two disconnected boundaries and a causally disconnected interior. In this paper, we argue that the connectedness properties of de Sitter space naturally encode the notion entanglement. We propose an holographic description of an inertial observer in terms of a thermofield double state in the tensor product of the past and future Hilbert spaces, whereby the Gibbons--Hawking formula arises as the holographic entanglement entropy between the past and future conformal boundaries. When considering the entanglement between the two interior Rindler wedges, we show--with no need of holography--that the entanglement entropy between two antipodal and causally disconnected observers is given by a quarter of the area of a pair minimal surfaces. These surfaces are the set of fixed points of an $S^2/mathbb Z_q$ orbifold and their total area, when restricted to a single Rindler wedge, reduces to the area of the cosmological horizon (hence recovering the Gibbons--Hawking area law).

We consider a deformed version of four-dimensional de Sitter spacetime. The setup consist of two (antipodal) disconnected Rindler observers, each one with an S-4 topology. We show that the two observers have an entanglement entropy, in the low energy sector, given by a quarter of the area of a pair minimal surfaces, that corresponds to the set of fixed points of an Z(q) orbifold. The result matches with the Gibbons-Hawking entropy when we restrict the Z(q) action to a single Rindler wedge.

In this thesis, we aim to understand the microscopic details and origin of the Cosmological Horizon, produced by a static observer in four-dimensional de Sitter (dS$_4$) spacetime. We consider a deformed extension of dS spacetime by means of a single $\mathbb Z_q$ quotient, which resembles an Orbifold geometry. The Orbifold parameter induces a pair of codimension two minimal surfaces given by 2-spheres in the Euclidean geometry. Using dimensional reduction on the two-dimensional plane where the minimal surfaces have support, we use the Liouville field theory and the Kerr/CFT mechanism in order to describe the underlying degrees of freedom of the Cosmological Horizon. We then show, that in the large $q$-limit, this pair of codimensions two surfaces can be realized as the conformal boundaries of dS$_3$. We notice that the central charge obtained using Liouville theory, in the latter limit, corresponds to the Strominger central charge obtained in the context of the dS/CFT correspondence. In addition, a formulation of entanglement entropy for de Sitter spacetimes is given in terms of dS holography and also a different approach in which the entanglement between two disconnected bulk observers is described in terms of the topology of the spacetime. Therefore, a quarter of the area formula is proposed, in which the area corresponds to the are of the set of fixed points of an $S^2/\mathbb Z_q$ orbifold.

In this work, we compute the conserved quantities of a charged rotating black hole which appears as the solution of Einstein-Maxwell action in five dimensions coupled to a Chern-Simons term for U(1) field. The addition of the Chern-Simons term will modify the Maxwell equations and the definition of charge but not the Einstein field equations. Upon the addition of suitable boundary terms for the pure gravity sector of the theory, which depend on the extrinsic and intrinsic curvatures (Kounterterms), we obtain the correct conserved quantities of the solution.