We study $AdS\times X$ null deformations arising as near horizon limits of D3-brane analogs of inhomogenous plane waves. Restricting to normalizable deformations for the $AdS_5$ case, these generically correspond in the dual field theory to SYM states with lightcone momentum density $T_{++}$ varying spatially, the homogenous case studied in arXiv:1202.5935 [hep-th] corresponding to uniform $T_{++}$. All of these preserve some supersymmetry. Generically these inhomogenous solutions exhibit analogs of horizons in the interior where a timelike Killing vector becomes null. From the point of view of $x^+$-dimensional reduction, the circle pinches off on these horizon loci in the interior. We discuss similar inhomogenous solutions with asymptotically Lifshitz boundary conditions, as well as aspects of Lifshitz singularities in string constructions involving $AdS$ null deformations. We also briefly discuss holographic entanglement entropy for some of these.
We compute entanglement entropy and differential entropy in inhomogeneous holographic quenches in AdS$_3$/CFT$_2$. The quenches are arbitrarily inhomogeneous and modeled by an infalling shell of massless non-rotating matter where the final state is not dual to a static black hole but rather to a black hole with time-dependent stress-energy tensor modes. We study the entanglement entropy of an interval and differential entropy of a family of intervals analytically when the inhomogeneities have a perturbative amplitude and numerically for non-perturbative inhomogeneities. While we are in princip…
We discuss some geometrical issues related to spacelike minimal surfaces in $AdS_m$ with null polygonal boundaries at conformal infinity. In particular for $AdS_4$, two holomorphic input functions for the Pohlmeyer reduced system are identified. This system contains two coupled differential equations for two functions $α(z,\bar z)$ and $β(z,\bar z)$, related to curvature and torsion of the surface. Furthermore, we conjecture that, for a polynomial choice of the two holomorphic functions, the relative positions of their zeros encode the conformal invariant data of the boundary null $2n$-gon.
For the asymptotic string solution in AdS_3 which is represented by the AdS_3 Poincare coordinates and yields the planar multi-gluon scattering amplitude at strong coupling in arXiv:0904.0663, we express it by the AdS_4 Poincare coordinates and demonstrate that the hexagonal and octagonal Wilson loops surrounding the string surfaces take closed contours consisting of null vectors in R^{1,2} owing to the relations of Stokes matrices. For the tetragonal Wilson loop we construct a string solution characterized by two parameters by solving the auxiliary linear problems and demanding a reality cond…
We consider null warped AdS(3) solutions of three-dimensional gravity coupled to a massive vector field. We isolate a certain set of non-propagating solutions to the equations of motion, which we argue are the ones relevant for understanding the stress tensor sector of the dual field theory. We construct a map from these modes to solutions of three-dimensional Einstein gravity with a negative cosmological constant, and thus show that they admit a Fefferman-Graham-like asymptotic expansion. We also compute the renormalized on-shell action for these modes at full non-linear level and propose tha…
We investigate the nature of the AdS/CFT duality between a subregion of the bulk and its boundary. In global AdS/CFT in the classical G_N=0 limit, the duality reduces to a boundary value problem that can be solved by restricting to one-point functions of local operators in the CFT. We show that the solution of this boundary value problem depends continuously on the CFT data. In contrast, the AdS-Rindler subregion cannot be continuously reconstructed from local CFT data restricted to the associated boundary region. Motivated by related results in the mathematics literature, we posit that a cont…
We describe solutions of 10-dimensional supergravity comprising null deformations of $AdS_5\times S^5$ with a scalar field, which have $z=2$ Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by dimensional reduction of these solutions. The dual field theory in this case is a deformation of the N=4 super Yang-Mills theory. We discuss the holographic 2-point function of operators dual to bulk scalars. We further describe time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling symmetries. We also discuss deformations of $AdS\times X$ in 11-dimensiona…
We study the null-polygonal minimal surfaces in AdS_4, which correspond to the gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces with n cusps is characterized by the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n-4)_4/U(1)^{n-5} generalized parafermion theory perturbed by the weight-zero adjoint operators. Based on the relation to the TBA systems of the perturbed W minimal models, we solve the TBA equations by using the conformal pe…
We consider AdS gravity duals to CFT on background spacetimes with a null infinity. Null infinity on the conformal boundary may extend to an extremal horizon in the bulk. For example it does so for Poincare-AdS, although does not for planar Schwarzschild-AdS. If null infinity does extend into an extremal horizon in the bulk, we show that the bulk near-horizon geometry is determined by the geometry of the boundary null infinity. Hence the `infra-red' geometry of the bulk is fixed by the large scale behaviour of the CFT spacetime. In addition the boundary stress tensor must have a particular dec…
We equip three-dimensional spin-3 gravity in the principal embedding with a new set of boundary conditions that we call "asymptotically null warped AdS". We find a chiral copy of the Polyakov-Bershadsky algebra as asymptotic symmetry algebra, reminiscent of the situation in topologically massive gravity with strict null warped AdS boundary conditions. We prove the invertibility of the map between zuvielbein and metric variables and construct a global gauge transformation to half of AdS spin-3 gravity in the diagonal embedding. This explains why the theory is chiral and why the Polyakov-Bershad…
Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations of $AdS_5\times X^5$ in Type IIB string theory sourced by a lightlike dilaton $Φ(x^+)$ dual to the N=4 super Yang-Mills theory with a lightlike varying gauge coupling. We argue that in the case where the $x^+$-direction is noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems with a potential in the $x^+$-direction generated by the lightlike dilaton. We then describe solutions of this sort with a linear dilaton. This enables a detailed calculation of 2-point correlation functions of operators…
We study the compatibility of the AdS/CFT duality with the bulk and boundary causality, and derive a conformally invariant averaged null energy condition (CANEC) for quantum field theories in 3 and 5-dimensional curved boundaries. This is the generalization of the averaged null energy condition (ANEC) in Minkowski spacetime to curved boundaries, where null energy is averaged along the null line with appropriate weight for conformal invariance. For this purpose we take, as our guiding principle, the no-bulk-shortcut theorem of Gao and Wald, which essentially asserts that when going from one poi…
We examine supersymmetric properties of null-warped AdS$_3$, or alternatively Schrodinger geometries, dual to putative warped CFTs in two dimensions. We classify super Schrodinger subalgebras of the superalgebra psu(1, 1$|$2) $\oplus$ psu(1, 1$|$2), corresponding to the superconformal algebra of the AdS$_3 \times$ S$^3$ geometry. We comment on geometric realisations and provide a string theory description with enhanced supersymmetry in terms of intersecting D3-branes. For type IIB supergravity solutions based on T$^{1,1}$, we consider the relationship between five-dimensional Schrodinger solut…
We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that the considered inhomogeneities typically become hydrodynamical earlier or at the same moment when hydrodynamics applies to the background, even though they decay slowly.
Massless spinning particle and tensionless string models on $AdS_d$ background in the projective-space realization are proposed as constrained Hamiltonian systems. Various forms of particle and string Lagrangians are derived and classical mechanics is studied including the Lax-type representation of the equations of motion. After that transition to the quantum theory is discussed. Analysis of potential anomalies in the tensionless string model necessitates introduction of ghosts and BRST charge. It is shown that quantum BRST charge is nilpotent for any $d$ if coordinate-momentum ordering for t…
In this paper, we examine the emergence of conserved charges on the horizon of a particular class of extremal non-dilatonic black $p$-branes (which reduce to extremal dilatonic black holes in $D=4$ dimensions upon toroidal compactification) in the presence of a probe massless scalar field in the bulk. This result is achieved by writing the black $p$-brane geometry in a Gaussian null coordinate system which allows us to get a non-singular near-horizon geometry description. We find that the near-horizon geometry is $AdS_{p+2}\times S^2$ and that the $AdS_{p+2}$ section has an internal structure …
We systematically search for classical open string solutions in AdS_3 within the general class expressed by elliptic functions (i.e., the genus-one finite-gap solutions). By explicitly solving the reality and Virasoro conditions, we give a classification of the allowed solutions. When the elliptic modulus degenerates, we find a class of solutions with six null boundaries, among which two pairs are collinear. By adding the S^1 sector, we also find four-cusp solutions with null boundaries expressed by the elliptic functions.
We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated …
In this note we consider minimal surfaces in three dimensional anti-de Sitter space that end at the AdS boundary on a polygon given by a sequence of null segments. The problem can be reduced to a certain generalized Sinh-Gordon equation and to SU(2) Hitchin equations. The mathematical problem to be solved arises also in the context of the moduli space of certain three dimensional supersymmetric theories. We can use explicit results available in the literature in order to find the explicit answer for the area of a surface that ends on a eight-sided null Wilson loop. Via the gauge/gravity dualit…
We write down Crofton formulas--expressions that compute lengths of spacelike curves in asymptotically AdS$_3$ geometries as integrals over kinematic space--which apply when the curve and/or the background spacetime is time-dependent. Relative to their static predecessor, the time-dependent Crofton formulas display several new features, whose origin is the local null rotation symmetry of the bulk geometry. In pure AdS$_3$ where null rotations are global symmetries, the Crofton formulas simplify and become integrals over the null planes, which intersect the bulk curve.
The holographic principle implies a vast reduction in the number of degrees of freedom of quantum gravity. This idea can be made precise in AdS_3, where the the stringy or gravitational exclusion principle asserts that certain perturbative excitations are not present in the exact quantum spectrum. We show that this effect is visible directly in the bulk gravity theory: the norm of the offending linearized state is zero or negative. When the norm is negative, the theory is signaling its own breakdown as an effective field theory; this provides a perturbative bulk explanation for the stringy exc…
We prove the achronal averaged null energy condition for general quantum field theories in the near horizon geometry of spherical extremal black holes (i.e. ${{\rm AdS}_2\times S^{d-2}}$), de Sitter and anti-de Sitter. The derivation follows from monotonicity of relative entropy after computing the modular hamiltonian of a null deformed region. For incomplete (but maximally extended) achronal null geodesics in ${\rm AdS}_2\times S^{d-2}$, we prove the positivity of a different light-ray operator for arbitrary CFTs. This agrees with a constraint recently derived for the Lorentzian cylinder.
We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincare-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of our previous paper arXiv:1806.08376, to the problem of how complexity of the CFT$_2$ groundstate changes under a small local conformal transformation according to the action (CA) prop…
The lightlike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. The solutions fall into two classes, depending on whether the Killing spinor is constant or not. In both cases, we give explicit examples of supersymmetric backgrounds. Among these BPS solutions, which preserve one quarter of the supersymmetry, there are gravitational waves propagating on domain walls or on bubbles of nothing that asymptote to AdS_4. Furthermore, we obtain the additional constraints obeyed by half…
Using the null-geodesic tunneling method of Parikh and Wilczek, we derive the Hawking temperature of a general four-dimensional rotating black hole. In order to eliminate the motion of $ϕ$ degree of freedom of a tunneling particle, we have chosen a reference system that is co-rotating with the black hole horizon. Then we give the explicit result for the Hawking temperature of the Kerr-Newman-AdS black hole from the tunneling approach.
We explore string/M-theory constructions of holographic theories with Lifshitz scaling exponent $z$ and hyperscaling violation exponent $θ$, finding a range of $z,θ$-values. Some of these arise as effective metrics from dimensional reduction of certain kinds of null deformations of $AdS$ spacetimes appearing in the near horizon geometries of extremal D3-, M2- and M5-brane theories. The $AdS_5$ solution in particular gives rise to $θ=1$ in $d=2$ (boundary) space dimensions. Other solutions arise as the IIA D2- and D4-brane solutions with appropriate null deformations, and we discuss the phase s…
The plane-wave limit of ${\rm AdS}_3 \times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1$ is analysed for generic null-geodesics that are not necessarily BPS. For the case of pure NS-NS flux it is shown how the resulting spectrum can be reproduced as a suitable limit of the world-sheet description in terms of WZW models. Since supersymmetry is broken, most of the degeneracies are lifted, and thus the identification of states is quite unambiguous.
We study integrable deformations of AdS/CFT by focusing upon three kinds of warped AdS_3 geometries, 1) space-like warped AdS_3, 2) time-like warped AdS_3 and 3) null warped AdS_3. These geometries are embedded into type IIB supergravity solutions and are regarded as consistent string backgrounds. By restricting the classical motion of strings on the warped AdS_3xS^1 subspace, the Landau-Lifshitz sigma models are derived by taking the fast-moving limit. The first two warped AdS_3 spaces correspond to anisotropic deformations of the sl(2) spin chain and the last one to Jordanian deformations. A…
We examine the achronal averaged null energy condition~(ANEC) for a class of conformal field theories~(CFT) at strong coupling in curved spacetime. By applying the AdS/CFT duality, we find holographic models which violate the achronal ANEC for $3+1$ and $4+1$-dimensional boundary theories. In our model, the bulk spacetime is an asymptotically AdS vacuum bubble solution with neither causality violation nor singularities. The conformal boundary of our bubble solution is asymptotically flat and is causally proper in the sense that a "fastest null geodesics" connecting any two points on the bounda…
We discuss dynamics of massive Klein-Gordon fields in two-dimensional Anti-de Sitter spacetimes ($AdS_2$), in particular conserved quantities and non-modal instability on the future Poincaré horizon called, respectively, the Aretakis constants and the Aretakis instability. We find out the geometrical meaning of the Aretakis constants and instability in a parallel-transported frame along a null geodesic, i.e., some components of the higher-order covariant derivatives of the field in the parallel-transported frame are constant or unbounded at the late time, respectively. Because $AdS_2$ is maxim…
We study classical open string solutions with a null polygonal boundary in AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS_n and generalized parafermions.
Using the Hubeny-Rangamani-Takayanagi (HRT) conjectured formula for entanglement entropy in the context of the AdS/CFT correspondence with time-dependent backgrounds, we investigate the relation between the bulk null energy condition (NEC) of the stress-energy tensor with the strong sub-additivity (SSA) property of entanglement entropy in the boundary theory. In a background that interpolates between an AdS to an AdS-Reissner-Nordstrom-type geometry, we find that generically there always exists a critical surface beyond which the violation of NEC would naively occur. However, the extremal area…
In this paper, we aim to examine the relationship between the unstable circular photon orbit and the thermodynamic phase transition for a rotating Kerr-AdS black hole. On one side, we give a brief review of the phase transition for the Kerr-AdS black hole. The coexistence curve and the metastable curve corresponding to the phase transition are clearly shown. On the other side, we calculate the radius and the angular momentum of the unstable circular orbits for a photon by analyzing the effective potential. Then combining these two sides, we find the following results. i) The radius and the ang…
We examine the five-region holographic entropy cone inequalities for the special case of the AdS$_3$-Vaidya metric for a variety of boundary configurations. This is done by numerically solving the geodesic equation in the bulk for various boundary configurations. In all the cases we examine, we find that all the inequalities are satisfied when the bulk satisfies the null energy condition, while the inequalities are all violated when the bulk spacetime violates the null energy condition. A proof of the five-region holographic entropy cone inequalities for the dynamical bulk case remains an open…
Starting from the averaged null energy condition (ANEC) in Minkowski we show that conformal symmetry implies the ANEC for a conformal field theory (CFT) in a de Sitter and anti-de Sitter background. A similar and novel bound is also obtained for a CFT in the Lorentzian cylinder. Using monotonicity of relative entropy, we rederive these results for dS and the cylinder. As a byproduct we obtain the vacuum modular Hamiltonian and entanglement entropy associated to null deformed regions of CFTs in (A)dS and the cylinder. A third derivation of the ANEC in dS is shown to follow from bulk causality i…
We study a toy model of the Kerr/CFT correspondence using string theory on AdS$_3 \times S^3$. We propose a single trace irrelevant deformation of the dual CFT generated by a vertex operator with spacetime dimensions (2,1). This operator shares the same quantum numbers as the integrable $T\bar{J}$ deformation of two-dimensional CFTs where $\bar{J}$ is a chiral $U(1)$ current. We show that the deformation is marginal on the worldsheet and that the target spacetime is deformed to null warped AdS$_3$ upon dimensional reduction. We also calculate the spectrum of the deformed theory on the cylinder…
We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT$_2$). We show that QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also addres…
We find that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value and the shadowless-ness may be related to the appearance of the null hypersurface caustics (NHC) both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
We present a complete study of the geodesics around naked singularities in AdS$_3$, the three-dimensional anti-de Sitter spacetime. These stationary spacetimes, characterized by two conserved charges --mass and angular momentum--, are obtained through identifications along spacelike Killing vectors with a fixed point. They are interpreted as massive spinning point particles, and can be viewed as three-dimensional analogues of cosmic strings in four spacetime dimensions. The geodesic equations are completely integrated and the solutions are expressed in terms of elementary functions. We classif…
