Dimensional Anti-de Sitter Spacetime Research Articles

Weak cosmic censorship with SU(2) gauge field and bound on charge-to-mass ratio

We numerically construct the stationary solutions of SU(2) Einstein-Yang-Mills theory in four dimensional anti-de Sitter spacetime. When the t component of the SU(2) gauge field is taken to the only nonzero component, we construct a class of counterexamples to the weak cosmic censorship conjecture in Einstein-Maxwell theory. However, including a nonzero ϕ component of SU(2) gauge field, we can argue that there is a minimum value qW, when the charge carried by the ϕ component is larger than this minimum value, for sufficiently large boundary electric amplitude a, the original counterexamples can be removed and cosmic censorship is preserved.

Fisher information of a black hole spacetime

Relativistic quantum metrology is the study of optimal measurement procedures within systems that have both quantum and relativistic components. Here we use Unruh-DeWitt detectors coupled to a massless scalar field as probes of thermal parameters in different spacetimes via a relativistic quantum metrology analysis. We consider both (2 + 1)-dimensional anti-de Sitter and BTZ black hole spacetimes. We compute the Fisher information to identify characteristics of the black hole spacetime and to compare it to a uniformly accelerating detector in anti-de Sitter space. We find the dependence of the Fisher information on temperature, detector energy gap, black hole mass, interaction time, and the initial state of the detector. We identify strategies that maximize the Fisher information and therefore the precision of estimation.

Deep learning metric detectors in general relativity

We consider conceptual issues of deep learning (DL) for metric detectors using test particle geodesics in curved spacetimes. Advantages of DL metric detectors are emphasized from a view point of general coordinate transformations. Two given metrics (two spacetimes) are defined to be conneted by a DL isometry if their geodesic image data cannot be discriminated by any DL metric detector at any time. The fundamental question of when the DL isometry appears is extensively explored. If the two spacetimes connected by the DL isometry are in superposition of quantum gravity theory, the post-measurement state may be still in the same superposition even after DL metric detectors observe the superposed state. We also demonstrate metric-detection DL's in 2+1 dimensional anti-de Sitter (AdS) spacetimes to estimate the cosmological constants and Brown-Henneaux charges. In the AdS/CFT correspondence dictionary, it may be expected that such metric detectors in the AdS bulk region correspond to quantum measurement devices in the CFT at the AdS boundary.

Ground state for the Klein-Gordon field in anti–de Sitter spacetime with dynamical Wentzell boundary conditions

We consider a real Klein-Gordon field in the Poincar\'e patch of $(d+1)$-dimensional anti-de Sitter spacetime, PAdS$_{d+1}$, and impose dynamical boundary condition on the asymptotic boundary of PAdS$_{d+1}$ that depend explicitly on the second time derivative of the field at the boundary. These boundary conditions are of generalized Wentzell type. We construct the Wightman two-point function for the ground state of the Klein-Gordon theory whenever the parameters of the theory (the field mass, curvature coupling and boundary condition parameters) render such ground state admissible. In the cases in which the mass of the Klein-Gordon field and the curvature coupling term yield an effectively massless theory, we can define a boundary field whose dynamics are ruled by the dynamical boundary condition and construct, in addition to the Wightman function for the Klein-Gordon field, boundary-to-boundary, boundary-to-bulk and bulk-to-boundary propagators.

AdS one-loop partition functions from bulk and edge characters

We show that the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss the relation between the character integral representation and the Rindler-AdS thermal partition function.

A group theoretical approach to quantum gravity in (A)dS

This thesis is devoted to developing a group-theoretical approach towards quantum gravity in (Anti)-de Sitter spacetime. We start with a comprehensive review of the representation theory of de Sitter (dS) isometry group, focusing on the construction of unitary irreducible representations and the computation of characters. The three chapters that follow present the results of novel research conducted as a graduate student. Chapter 4 is based on [1]. We provide a general algebraic construction of higher spin quasinormal modes of de Sitter horizon and identify the boundary operator insertions that source the quasinormal modes from a local QFT point of view. Quasinormal modes of a single higher spin field in dSD furnish two nonunitary lowest-weight representations of the dS isometry group SO(1,D). We also show that quasinormal mode spectrums of higher spin fields are precisely encoded in the Harish-Chandra characters of the corresponding SO(1,D) unitary irreducible representations. Chapter 5 is based on work with D. Anninos, F. Denef and A. Law [2]. With potential application to constraining UV-complete microscopic models of de Sitter quantum gravity, we compute de Sitter entropy as the logarithm of the sphere path integral, for any possible low energy effective field theory containing a massless graviton, in arbitrary dimensions. The path integral is performed exactly at the one-loop level. The one-loop correction to the dS entropy is found to take a universal “bulk−edge” form, with the bulk part being an integral transformation of a Harish-Chandra character encoding quasinormal modes spectrum in a static patch of dS and the edge part being the same integral transformation of an edge character encoding degrees of freedom frozen on the dS horizon. In 3D de Sitter spacetime, the one-loop exact entropy is promoted to an all-loop exact result for truncated higher spin gravity, the latter admitting an SL(n,C) Chern-Simons formulation with n being the spin cut-off. Chapter 6 is based on [3]. Inspired by [2], we revisit the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime and show that it can be universally expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higherspin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters, leading to striking agreement with the predictions of higher spin holography. We also comment on the relation between our character integral formula and Rindler-AdS [4] thermal partition functions.

Accelerated paths and Unruh effect. Part I. Scalars and fermions in Anti De Sitter spacetime

We have investigated the Unruh effect in Anti de-Sitter (AdS) spacetime by examining the response function of an Unruh-DeWitt particle detector with uniform constant acceleration. An exact expression of the detector response function for the scalar field has been obtained with different levels of non-linearity in even dimensional AdS spacetime. We also showed how the response of the accelerated Unruh detector coupled quadratically to massless Dirac field in D dimensional (D ≥ 2) AdS spacetime is proportional to that of a detector linearly coupled to a massless scalar field in 2D dimensional AdS spacetime. Here, the fermionic and scalar matter field is coupled minimally and conformally to the background AdS metric, respectively. Finally, we discuss about the extension of the results for more general stationary motion.

Regularization ambiguity and van der Waals black hole in 2 + 1 dimensions

Charged black holes in a (2+1)-dimensional anti-de Sitter space-time suffer from some limitations such as the ambiguity in the definition of the mass and the bad short distance behavior. In this paper we present a way to resolve such issues. By extending the parameter space of the BTZ geometry, we properly identify the integration constants in order to remove the conical singularity sitting at the origin. In such a way we obtain a well defined Minkowski limit and horizons also in the case of de Sitter background space. On the thermodynamic side, we obtain a proper internal energy, by invoking the consistency with the Area Law, even if the mass parameter does not appear in the metric coefficients. As a further improvement, we show that it is sufficient to assume a finite size of the electric charge to obtain a short scale regular geometry. The resulting solution, generalizing the charged BTZ metric, is dual to a van der Waals gas.

Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of (4+1)-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z2-symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. The only nonzero component of the current density is along the azimuthal direction and in both the regions the corresponding VEV is decomposed into the brane- free and brane-induced contributions. The latter vanishes on the string and near the string the total current is dominated by the brane-free part. At large distances from the string and in the region between the brane and AdS horizon the decay of the brane-induced current density, as a function of the proper distance, is power-law for both massless and massive fields. For a massive field this behavior is essentially different from that in the Minkowski bulk. In the region between the brane and AdS boundary the large-distance decay of the current density is exponential. Depending on the boundary condition on the brane, the brane-induced contribution is dominant or subdominant in the total current density at large distances from the string. By using the results for fields realizing two inequivalent irreducible representations of the Clifford algebra, the vacuum current density is investigated in C - and P -symmetric fermionic models. Applications are given for a cosmic string in the Randall-Sundrum-type braneworld model with a single brane.

Study on a holographic static transverse polarization at non-zero temperature

The analytical structure of a static transverse component of polarization tensor in complex momentum plane is numerically studied, which is holographically determined by a Einstein-Maxwell theory in asymptotically D=3+1 dimensional Anti-de Sitter spacetime. This strongly-coupled transverse polarization shows a pair of conjugate simple poles on the imaginary-axis at low temperature, which is different with the longitudinal component of the corresponding polarization and the counterpart in its weakly-coupled version.

Catalytic creation of baby bubble universe with small positive cosmological constant

We investigate the decay of metastable de Sitter, Minkowski and anti-de Sitter vacua catalyzed by a black hole and a cloud of strings. We apply the method to the creation of the four dimensional bubble universe in the five dimensional anti-de Sitter spacetime recently proposed by Banerjee, Danielsson, Dibitetto, Giri and Schillo [1, 2]. We study the bounce action for the creation and find that the bubble with very small cosmological constant, of order Λ(4)/ {M}_4^4 ∼ 10−120, is favored by the catalysis by assuming appropriate mass scales of the black hole and the cloud of strings to reproduce the present energy densities of matter and radiation in the bubble universe.

Comment on “Hadamard states for a scalar field in anti–de Sitter spacetime with arbitrary boundary conditions”

In a recent paper (Phys. Rev. D 94, 125016 (2016)), the authors argued that the singularities of the two-point functions on the Poincar\'e domain of the $n$-dimensional anti-de Sitter spacetime ($\text{PAdS}_n$) have the Hadamard form, regardless of which (Robin) boundary condition is chosen at the conformal boundary. However, the argument used to prove this statement was based on an incorrect expression for the two-point function $G^{+}(x,x')$, which was obtained by demanding $\text{AdS}$ invariance for the vacuum state. In this comment I show that their argument works only for Dirichlet and Neumann boundary conditions and that the full $\text{AdS}$ symmetry cannot be respected by nontrivial Robin conditions (i.e., those which are neither Dirichlet nor Neumann). By studying the conformal scalar field on $\text{PAdS}_2$, I find the correct expression for $G^{+}(x,x')$ and show that, notwithstanding this problem, it still have the Hadamard form.

Physical generalizations of the Rényi entropy

We present a new type of generalization of the Rényi entropy that follows naturally from its representation as a thermodynamic quantity. We apply it to the case of [Formula: see text]-dimensional conformal field theories (CFTs) reduced on a region bounded by a sphere. It is known how to compute their Rényi entropy as an integral of the thermal entropy of hyperbolic black holes in [Formula: see text]-dimensional anti-de Sitter spacetime. We show how this integral fits into the framework of extended gravitational thermodynamics, and then point out the natural generalization of the Rényi entropy that suggests itself in that light. In the field theory terms, the new generalization employs aspects of the physics of Renormalization Group (RG) flow to define a refined version of the reduced vacuum density matrix. For [Formula: see text], it can be derived directly in terms of twist operators in field theory. The framework presented here may have applications beyond this context, perhaps in studies of both quantum and classical information theoretic properties of a variety of systems.

Holographic heat engines, entanglement entropy, and renormalization group flow

We explore a fruitful connection between the physics of conformal field theories (CFTs) in -dimensional Minkowski spacetime and the extended gravitational thermodynamics of hyperbolic black holes in -dimensional anti-de Sitter spacetime. The CFTs are reduced on a region bounded by a sphere. We show that renormalization group flows between CFTs are specific thermodynamic processes in the plane, where the irreversibility of coarse-graining flows from the ultraviolet to the infrared corresponds to the second law of thermodynamics, preventing heat from flowing from low temperature to high. We observe that holographic heat engines using the black holes as a working substance correspond to specific combinations of CFT flows and deformations. We construct three special engines whose net heat and work can be described in terms of changes of entanglement entropy across the sphere. Engine efficiencies emerge as simple functions of the ratio of the number of degrees of freedom of two CFTs.

Character integral representation of zeta function in AdSd+1. Part I. Derivation of the general formula

The zeta function of an arbitrary field in (d + 1)-dimensional anti-de Sitter (AdS) spacetime is expressed as an integral transform of the corresponding so(2, d) representation character, thereby extending the results of [arXiv:1603.05387] for AdS4 and AdS5 to arbitrary dimensions. The integration in the variables associated with the so(d) part of the character can be recast into a more explicit form using derivatives. The explicit derivative expressions are presented for AdSd+1 with d = 2, 3, 4, 5, 6.

Superstrings on AdS3 at k = 1

We study superstring theory in three dimensional Anti-de Sitter spacetime with NS-NS flux, focusing on the case where the radius of curvature is equal to the string length. This corresponds to the critical level k = 1 in the formulation as a Wess-Zumino-Witten model. Previously, it was argued that a transition takes place at this special radius, from a phase dominated by black holes at larger radius to one dominated by long strings at smaller radius. We argue that the infinite tower of modes that become massless at k = 1 is a signal of this transition. We propose a simple two-dimensional conformal field theory as the holographic dual to superstring theory at k = 1. As evidence for our conjecture, we demonstrate that our putative dual exactly reproduces the full spectrum of the long strings of the weakly coupled string theory, including states unprotected by supersymmetry.

Rigidity of isometric immersions into the light cone

In this paper, we show the rigidity of isometric immersions for a Riemannian manifold of dimension $n-1$ into the light cone of $n+1$ dimensional Minkowski, de Sitter and anti-de Sitter spacetimes for $n\geq 3$.

Character integral representation of zeta function in AdSd+1. Part II. Application to partially-massless higher-spin gravities

We compute the one-loop free energies of the type-Aℓ and type-Bℓ higher-spin gravities in (d + 1)-dimensional anti-de Sitter (AdSd+1) spacetime. For large d and ℓ, these theories have a complicated field content, and hence it is difficult to compute their zeta functions using the usual methods. Applying the character integral representation of zeta function developed in the companion paper [arXiv:1805.05646] to these theories, we show how the computation of their zeta function can be shortened considerably. We find that the results previously obtained for the massless theories (ℓ = 1) generalize to their partially-massless counterparts (arbitrary ℓ) in arbitrary dimensions.

Perturbations of spiky strings in AdS3

Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further demonstrate that there do exist finite perturbations of the AdS spiky strings. Our results therefore establish that the spiky string configurations in AdS3 are indeed stable against small fluctuations. Comments on future possibilities of work are included in conclusion.

Fast and slow coherent cascades in anti-de Sitter spacetime

We study the phase and amplitude dynamics of small perturbations in 3 + 1 dimensional anti-de Sitter spacetime using the truncated resonant approximation, also known as the two time framework. We analyse the phase spectrum for different classes of initial data and find that higher frequency modes turn on with coherently aligned phases. Combining numerical and analytical results, we conjecture that there is a class of initial conditions that collapse in infinite slow time and to which the well-studied case of the two-mode, equal energy initial data belongs. We additionally study perturbations that collapse in finite time, and find that the energy spectrum approaches a power law, with the energy per mode scaling approximately as the inverse first power of the frequency.