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The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N holographic theories, these fundamental observables are dual to the open-string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions — conformal invariance of the line defect, large N factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique. [ABSTRACT FROM AUTHOR]

Quantum complexity has already shed light on CFT states dual to bulk geometries containing spacelike singularities [1–3]. In this work, we turn our attention to the quantum complexity of CFT/quantum gravity states which are dual to bulk geometries containing a naked timelike singularity. The appearance of naked timelike singularities in semiclassical gravity is allowed in string theory, particularly in the context of holography, so long as they satisfy the Gubser criterion [4-5] — those naked timelike singularities which arise as the extremal limits of geometries containing cloaked singularities are admissible. In this work, we use holographic complexity as a probe on geometries containing naked timelike singularities and explore potential relation to the Gubser criterion for detecting allowable naked timelike singularities. We study three specific cases of naked timelike singularities, namely the negative mass Schwarzschild-AdS spacetime, the timelike Kasner-AdS [6] and Einstein-dilaton system [7]. The first two cases are outright ruled out by the Gubser criterion while the third case is more subtle — according to the Gubser criterion the singularity switches from forbidden to admissible as the parameter α is dialed in the range [0, 1] across the transition point at α = 1 / 3 . We probe all three geometries using two holographic complexity prescriptions, namely CA and CV. For the case of the negative mass SAdS and timelike Kasner-AdS4 the complexities display no sign of pathology (both receive finite contribution from the naked singularity). For the Einstein-Dilaton case, action-complexity does display a sharp transition from physical positive values to patholgical negative divergent values (arising from the singularity) as one transcends the Gubser bound. Our study suggests that neither action-complexity (CA) nor volume-complexity (CV) can serve as a sensitive tool to investigate (naked) timelike singularities. [ABSTRACT FROM AUTHOR]

A long-standing and intriguing question is: does the holographic principle apply to cosmologies like de Sitter spacetime? In this work, we consider a half dS spacetime wherein a timelike boundary encloses the bulk spacetime, presenting a version of de Sitter holography. By analyzing the holographic entanglement entropy in this space and comparing it with that in AdS/CFT, we argue that gravity on a half dSd+1 is dual to a highly non-local field theory residing on dSd boundary. This non-locality induces a breach in the subadditivity of holographic entanglement entropy. Remarkably, this observation can be linked to another argument that time slices in global de Sitter space overestimate the degrees of freedom by redundantly counting the same Hilbert space multiple times. [ABSTRACT FROM AUTHOR]

We compute all worldsheet three-point functions involving spectrally-flowed operators in chiral multiplets of the space-time theory for strings in AdS3×S3×T4, thus completing the analysis of the full AdS3/CFT2 chiral ring. We make use of techniques recently developed for the bosonic sector, based on holomorphic covering maps from the worldsheet to the AdS3 boundary. We highlight the role of the so-called series identifications when dealing with the complications originated by picture-changing spectrally-flowed states. We find an exact agreement with the predictions from the holographic CFT at the symmetric orbifold point. [ABSTRACT FROM AUTHOR]

Based on the AdS/CFT correspondence, we study how to reconstruct bulk spacetime metrics by various quantum information measures on the boundary field theories, which include entanglement entropy, mutual information, entanglement of purification, and computational complexity according to the proposals of complexity=volume 2.0 and complexity=generalized volume. We present several reconstruction methods, all of which are free of UV divergence and most of which are driven by the derivatives of the measures with respect to the boundary scales. We illustrate that the exterior and interior of a black hole can be reconstructed using the measures of spatial entanglement and time-evolved complexity, respectively. We find that these measures always probe the spacetime in a local way: reconstructing the bulk metric in different radial positions requires the information at different boundary scales. We also show that the reconstruction method using complexity=volume 2.0 is the simplest and has a certain strong locality. [ABSTRACT FROM AUTHOR]

An important problem in Quantum Field Theory (QFT) is to understand the structures of observables on spacetime manifolds of nontrivial topology. Such observables arise naturally when studying physical systems at finite temperature and/or finite volume and encode subtle properties of the underlying microscopic theory that are often obscure on the flat spacetime. Locality of the QFT implies that these observables can be constructed from more basic building blocks by cutting-and-gluing along a spatial slice, where a crucial ingredient is the Hilbert space on the spatial manifold. In Conformal Field Theory (CFT), thanks to the operator-state correspondence, we have a non-perturbative understanding of the Hilbert space on a spatial sphere. However it remains a challenge to consider more general spatial manifolds. Here we study CFTs in spacetime dimensions d > 2 on the spatial manifold T2 × ℝd−3 which is one of the simplest manifolds beyond the spherical topology. We focus on the ground state in this Hilbert space and analyze universal properties of the ground state energy, also commonly known as the Casimir energy, which is a nontrivial function of the complex structure moduli τ of the torus. The Casimir energy is subject to constraints from modular invariance on the torus which we spell out using PSL(2, ℤ) spectral theory. Moreover we derive a simple universal formula for the Casimir energy in the thin torus limit using the effective field theory (EFT) from Kaluza-Klein reduction of the CFT, with exponentially small corrections from worldline instantons. We illustrate our formula with explicit examples from well-known CFTs including the critical O(N) model in d = 3 and holographic CFTs in d ≥ 3. [ABSTRACT FROM AUTHOR]

We explore the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and AdS3 in the IR, and single-trace T T ¯ deformed CFT. In particular, we explain how the deformation of states in the boundary theory is reflected in the bulk geometry, and show that the coupling above which the deformed energy of the SL(2, ℝ) invariant ground state of the IR CFT becomes complex is a maximal coupling. [ABSTRACT FROM AUTHOR]

Using the AdS/CFT correspondence we model the behaviour of the two-point correlator of an operator with arbitrary scale dimension ∆ in arbitrary spacetime dimension d for small but non-zero temperature. The obtained propagator coincides in the low temperature regime with the known result for d = 4 for large ∆ at the order Td as well as with the Td and T2d terms of the exact all order result for d = 2. Furthermore, for arbitrary d we explicitly write down the expression for the order Td of the propagator for arbitrary ∆, and present a conjecture for the order T2d in the large ∆ limit. [ABSTRACT FROM AUTHOR]

We extend in two directions our recent investigation of strongly interacting quantum fields in a class of spacetimes with chronology horizons (Misner spacetimes). First, we generalize to arbitrary dimensions the holographic mechanism of chronology protection in the absence of gravitational backreaction. The AdS geometry dual to a conformal field theory in these spacetimes shows, in every dimension, an entire separation between the bulk duals of the chronal and non-chronal regions, with the former being complete, regular geometries. In some instances the protection requires the inclusion of non-planar CFT corrections, which we obtain using double holography. Second, we compute the gravitational backreaction of the quantum fields in the Misner-AdS3 spacetime, and show that the null chronology horizon turns into a strong, spacelike curvature singularity. This is one of the few controlled, explicit examples where we can see quantum effects change a Cauchy horizon into a spacelike singularity. [ABSTRACT FROM AUTHOR]

Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra. [ABSTRACT FROM AUTHOR]

We study how coarse-graining procedure of an underlying UV-complete quantum gravity gives rise to a connected geometry. It has been shown, quantum entanglement plays a key role in the emergence of such a geometric structure, namely a smooth Einstein-Rosen bridge. In this paper, we explore the possibility of the emergence of similar geometric structure from classical correlation, in the AdS/CFT setup. To this end, we consider a setup where we have two decoupled CFT Hilbert spaces, then choose a random typical state in one of the Hilbert spaces and the same state in the other. The total state in the fine-grained picture is of course a tensor product state, but averaging over the states sharing the same random coefficients creates a geometric connection for simple probes. Then, the apparent spatial wormhole causes a factorization puzzle. We argue that there is a spatial analog of half-wormholes, which resolves the puzzle in the similar way as the spacetime half-wormholes. [ABSTRACT FROM AUTHOR]

Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the energy spectrum of QFTs in two-dimensional AdS. The infinite volume of constant timeslices of AdS leads to divergences in the energy levels. We propose a simple prescription to obtain finite physical energies and test it with numerical diagonalization in several models: the free massive scalar field, ϕ4 theory, Lee-Yang and Ising field theory. Along the way, we discuss spontaneous symmetry breaking in AdS and derive a compact formula for perturbation theory in quantum mechanics at arbitrary order. Our results suggest that all conformal boundary conditions for a given theory are connected via bulk renormalization group flows in AdS. [ABSTRACT FROM AUTHOR]

The extended BMS algebra contains a conformal subgroup that acts on the celestial sphere as SO(1, 3). It is of interest to perform mode expansions of free fields in Minkowski spacetime that realize this symmetry in a simple way. In the present work we perform such a mode expansion for massive scalar fields using the unitary principal series representations of SO(1, 3) with a view to developing a holographic approach to gravity in asymptotically flat spacetime. These mode expansions are also of use in studying holography in three-dimensional de Sitter spacetime. [ABSTRACT FROM AUTHOR]

In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor ℭα(n)(h) is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential hα(n). The explicit form of ℭα(n)(h) is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for ℭα(n)(h) in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action S CS n h ∝ ∫ d 3 xeh α n ℭ α n h factorises into a product of (n − 1) first-order operators that are associated with the spin-n/2 partially massless AdS values. Our findings greatly facilitate the on-shell analysis of massive higher-spin gauge-invariant actions in AdS3. The main results are extended to the case of N = 1 AdS supersymmetry. In particular, we derive simple expressions for the higher-spin super-Cotton tensors in AdS3. [ABSTRACT FROM AUTHOR]

We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss the systematic expansion in large intermediate spin and the resummations of the large-spin tails of Regge trajectories. The basic integrals for the Lorentzian inversion are given by Wilson functions. [ABSTRACT FROM AUTHOR]

In this paper, we explore the open string amplitude's dual role as a space-time S-matrix and a 2D holomorphic CFT correlation function. We pursue this correspondence in two directions. First, beginning with a general disk integrand dressed with a Koba-Nielsen factor, we demonstrate that exchange symmetry for the factorization residue of the amplitude forces the integrand to be expandable on SL(2,R) conformal blocks. Furthermore, positivity constraints associated with unitarity imply the SL(2,R) blocks must come in linear combinations for which the Virasoro block emerges at the "kink" in the space of solutions. In other words, Virasoro symmetry arises at the boundary of consistent factorization. Next, we consider the low energy EFT description, where unitarity manifests as the EFThedron in which the couplings must live. The existence of a worldsheet description implies, through the Koba-Nielsen factor, monodromy relations which impose algebraic identities amongst the EFT couplings. We demonstrate at finite derivative order that the intersection of the "monodromy plane" and the four-dimensional EFThedron carves out a tiny island for the couplings, which continues to shrink as the derivative order is increased. At the eighth derivative order, on a three-dimensional monodromy plane, the intersection fixes the width of this island to around 1.5% (of ζ(3)) and 0.2% (of ζ(5)) with respect to the toroidally compactified Type-I super string answer. This leads us to conjecture that the four-point open superstring amplitude can be completely determined by the geometry of the intersection of the monodromy plane and the EFThedron. [ABSTRACT FROM AUTHOR]

We generalize the Gao-Jafferis-Wall construction of traversable two-sided wormholes to multi-boundary wormholes. In our construction, we take the background spacetime to be multi-boundary black holes in AdS3. We work in the hot limit where the dual CFT state in certain regions locally resembles the thermofield double state. Furthermore, in these regions, the hot limit makes the causal shadow exponentially small. Based on these two features of the hot limit, and with the three-boundary wormhole as our main example, we show that traversability between any two asymptotic regions in a multi-boundary wormhole can be triggered using a double-trace deformation. In particular, the two boundary regions need not have the same temperature and angular momentum. We discuss the non-trivial angular dependence of traversability in our construction, as well as the effect of the causal shadow region. [ABSTRACT FROM AUTHOR]

We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field ϕ, in the (3 + 1)-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to ϕ†ϕ. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behaved results. The regularised result also contains a de Sitter symmetry breaking logarithm, growing with the cosmological time. Possibility of extension of these results with the so called de Sitter α-vacua is discussed. While we find no apparent problem in computing the response function for a real scalar in these vacua, a complex scalar field is shown to contain some possible ambiguities in the detector response. The case of the minimal and nearly massless scalar field theory is also briefly discussed. [ABSTRACT FROM AUTHOR]

We explicitly rewrite the path integral for the free or critical O(N) (or U(N)) bosonic vector models in d space-time dimensions as a path integral over fields (including massless high-spin fields) living on (d + 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large N limit to Vasiliev's classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account. [ABSTRACT FROM AUTHOR]

We propose a non-unitary example of holography for the family of two-dimensional logarithmic conformal field theories with negative central charge c = cp,1 = −6p + 13 − 6p−1. We argue that at large p, these models have a semiclassical gravity-like description which contains, besides the global AdS3 spacetime, a tower of solitonic solutions describing conical excess angles. Evidence comes from the fact that the central charge and the natural modular invariant partition function of such a theory coincide with those of the cp,1 model. These theories have an extended chiral W-algebra whose currents have large spin of order |c|, and which in the bulk are realized as spinning conical solutions. As a by-product we also find a direct link between geometric actions for exceptional Virasoro coadjoint orbits, which describe fluctuations around the conical spaces, and Felder's free field construction of degenerate representations. [ABSTRACT FROM AUTHOR]

We study singular time-dependent 1 8 -BPS configurations in the abelian sector of N = 4 supersymmetric Yang-Mills theory that represent BPS string-like defects in ℝ × S3 spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to 1 8 -BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global AdS5 × S5 that share supersymmetries with a class of dual-giant gravitons. For simple configurations, we demonstrate how to define a good variational problem and propose a regularization scheme that leads to finite energy and global charges on both sides of the holographic correspondence. [ABSTRACT FROM AUTHOR]

We conjecture a simple set of "Feynman rules" for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the "OPE channel." The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper. [ABSTRACT FROM AUTHOR]

We compute fluctuations in the modular energy of the vacuum associated with a Rindler-wedge in AdS spacetime in the context of AdS/CFT. We discuss the possible effect of these energy fluctuations on the spacetime geometry, and on the traversal time of a light beam propagating from the boundary to the bulk and back. [ABSTRACT FROM AUTHOR]

We initiate a study of subregion dualities, entropy, and redundant encoding of bulk points in holographic theories deformed by T T ¯ and its generalizations. This includes both cut off versions of Anti de Sitter spacetime, as well as the generalization to bulk de Sitter spacetime, for which we introduce two additional examples capturing different patches of the bulk and incorporating the second branch of the square root dressed energy formula. We provide new calculations of entanglement entropy (EE) for more general divisions of the system than the symmetric ones previously available. We find precise agreement between the gravity side and deformed-CFT side results to all orders in the deformation parameter at large central charge. An analysis of the fate of strong subadditivity for relatively boosted regions indicates nonlocality reminiscent of string theory. We introduce the structure of operator algebras in these systems. The causal and entanglement wedges generalize to appropriate deformed theories but exhibit qualitatively new behaviors, e.g. the causal wedge may exceed the entanglement wedge. This leads to subtleties which we express in terms of the Hamiltonian and modular Hamiltonian evolution. Finally, we exhibit redundant encoding of bulk points, including the cosmological case. [ABSTRACT FROM AUTHOR]

Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model. [ABSTRACT FROM AUTHOR]

Recently, it is found that when an external magnetic field parallel to the boundary is applied, Weyl anomaly gives rises to a new anomalous current transport in the vicinity of the boundary. At the leading order of closeness from the boundary, the current is determined universally by the central charge of the theory. In this paper, we give a holographic proof for the existence and universality for this transport phenomena. We show that the current is independent of boundary conditions in four dimensions while it depends on boundary conditions in other dimensions. We also study the backreaction of the bulk Maxwell fields on the AdS spacetime and obtain the holographic Weyl anomaly for 5d BCFTs in presence of the background field strength. [ABSTRACT FROM AUTHOR]

We study the evolution of holographic subregion complexity under a thermal quench in this paper. From the subregion CV proposal in the AdS/CFT correspondence, the subregion complexity in the CFT is holographically captured by the volume of the codimension-one surface enclosed by the codimension-two extremal entanglement surface and the boundary subregion. Under a thermal quench, the dual gravitational configuration is described by a Vaidya-AdS spacetime. In this case wefind that the holographic subregion complexity always increases at early time, and after reaching a maximum it decreases and gets to saturation. Moreover we notice that when the size of the strip is large enough and the quench is fast enough, in AdSd+1(d ≥ 3) spacetime the evolution of the complexity is discontinuous and there is a sudden drop due to the transition of the extremal entanglement surface. We discuss the effects of the quench speed, the strip size, the black hole mass and the spacetime dimension on the evolution of the subregion complexity in detail numerically. [ABSTRACT FROM AUTHOR]

We construct solutions to the Einstein equations for asymptotically locally Anti-de Sitter spacetimes with four, five, and six dimensional Reissner-Nordström boundary metrics. These spacetimes are gravitational duals to 'jammed' CFTs on those backgrounds at infinite N and strong coupling. For these spacetimes, we calculate the boundary stress tensor as well as compute entanglement entropies for ball shaped regions as functions of the boundary black hole temperature T . From this, we see how the CFT prevents heat flow from the black hole to the vacuum at spatial infinity. We also compute entanglement entropies for a three dimensional boundary black hole using the AdS C-metric. We compare our results to previous work done in similar spacetimes. [ABSTRACT FROM AUTHOR]

We revisit the 1/2-BPS D-branes on the AdS×S background. Based only on the classification of 1/2-BPS D-branes obtained by the covariant open string description, we consider various purely static configurations of D-branes without any worldvolume flux on the AdS×S background. Under the covariant κ symmetry fixing condition, we investigate which part the spacetime supersymmetries is preserved on the D-brane worldvolume and obtain the associated worldvolume supersymmetry transformation rules to leading order in the worldvolume fluctuating fields. It is shown that, for purely static configurations without any worldvolume flux, only the AdS type D-branes, in which the AdS radial direction is one of worldvolume coordinates, are 1/2-BPS. [ABSTRACT FROM AUTHOR]

We present a formula for the information metric on ℝ × S for a scalar primary operator of integral dimension $$ \Delta\ \left(>\frac{d+1}{2}\right) $$ . This formula is checked for various space-time dimensions d and Δ in the field theory side. We check the formula in the gravity side using the holographic setup. We clarify the regularization and renormalization involved in these computations. We also show that the quantum information metric of an exactly marginal operator agrees with the leading order of the interface free energy of the conformal Janus on Euclidean S , which is checked for d = 2 , 3. [ABSTRACT FROM AUTHOR]

We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space - the natural setting for describing conformal field theories in two fewer dimensions. These theories have a SL(2) algebra of local bosonic constraints which can be supplemented by additional fermionic constraints depending on the matter content of the theory. By computing the BRST charge associated with gauge fixing these constraints, we find anomalies which vanish for specific target space dimensions. These critical dimensions coincide precisely with those for which (biadjoint) cubic scalar theory, gauge theory and gravity are classically conformally invariant. Furthermore, the BRST cohomology of each theory contains vertex operators for the full conformal multiplets of single field insertions in each of these space-time CFTs. We give a prescription for the computation of three-point functions, and compare our formalism with the scattering equations approach to on-shell amplitudes. [ABSTRACT FROM AUTHOR]

We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality 〈 T 〉 ≥ − C/L , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the 'conformal collider' constraints of Hofman and Maldacena. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right. [ABSTRACT FROM AUTHOR]

The AdS soliton is a nonsingular spacetime that has a flat conformal boundary with a compact S1 direction. We find a horizonless cohomogeneity-1 metric that describes nonlinear gravitational oscillations of the AdS soliton in five dimensions. We call this spacetime the resonating AdS soliton. This solution is obtained as the nonlinear extension of normal modes of the AdS soliton dual to spin-2 glueball excitations. The boundary energy momentum tensor of the resonating AdS soliton has time periodic components, and it is interpreted as a coherently excited state in the dual field theory. Physical quantities of the resonating AdS soliton are multivalued at a fixed energy, suggesting a transition between different frequency solutions. The energy of the resonating AdS soliton is higher than that of the undeformed AdS soliton, in accordance with the positive energy conjecture proposed by Horowitz and Myers. [ABSTRACT FROM AUTHOR]

In the action-complexity proposal there are two different methods to regularize the gravitational on-shell action, which are equivalent in the framework of AdS/CFT. In this paper, we want to study the equivalence of them for a pure BTZ black hole microstate. The microstate is obtained from a two-sided BTZ black hole truncated by a dynamical timelike ETW brane. Moreover, it is dual to a finite energy pure state in a two-dimensional CFT. We show that if one includes the timelike counterterms inspired by holographic renormalization as well as the Gibbons-Hawking-York term on the timelike boundary of the WDW patch, which exists in one of the regularizations, the coefficients of the UV divergent terms of action-complexity in the two methods become equal to each other. Furthermore, we compare the finite terms of action-complexity in both regularizations, and show that when the UV cutoff surface is close enough to the asymptotic boundary of the bulk spacetime, action-complexities in both regularizations become exactly equal to each other. [ABSTRACT FROM AUTHOR]

In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function F4. We also construct its generalization to the non-local primary exchange operator with continuous spin and its corresponding Mellin representation which are relevant for Lorentzian spacetime. Using these results we apply the Lorentzian inversion formula to compute the so-called crossing kernel in general spacetime dimensions, the resultant expression can be written as a double infinite summation over certain Kampé de Fériet hypergeometric functions with the correct double trace operator singularity structures. We also include some complementary computations in AdS space, demonstrating the orthogonality of conformal blocks and performing the decompositions. [ABSTRACT FROM AUTHOR]

According to AdS/CFT duality semi-classical strings in the Schrodinger space- time is conjectured to be a holographic dual to dipole CFT. In this paper we consider pulsating strings in five-dimensional Schrodinger space times five-sphere. We have found classical string solutions pulsating entirely in the Schrodinger part of the background. We quantize the theory semi-classically and obtain the wave function of the problem. We have found the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT. [ABSTRACT FROM AUTHOR]

Massless scattering amplitudes in four-dimensional Minkowski spacetime can be Mellin-transformed to correlation functions on the celestial sphere at null infinity called celestial amplitudes. We study various properties of massless four-point scalar and gluon celestial amplitudes such as conformal partial wave decomposition, crossing relations and optical theorem. As a byproduct, we derive the analog of the single and double soft limits for all gluon celestial amplitudes. [ABSTRACT FROM AUTHOR]

We study a toy model of the Kerr/CFT correspondence using string theory on AdS3 × S3. 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 TJ¯ deformation of two-dimensional CFTs where 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 AdS3 upon dimensional reduction. We also calculate the spectrum of the deformed theory on the cylinder and compare it to the field theory analysis of TJ¯-deformed CFTs. [ABSTRACT FROM AUTHOR]

We use holography to study sound modes of strongly-interacting conformal field theories with non-zero temperature, T, and U(1) chemical potential, μ. Specifically, we consider charged black brane solutions of Einstein gravity in (3+1)-dimensional Anti-de Sitter space coupled to a U(1) gauge field with Dirac-Born-Infeld action, representing a spacetime-filling brane. The brane action has two free parameters: the tension and the non-linearity parameter, which controls higher-order terms in the field strength. For all values of the tension, non-linearity parameter, and T /μ, and at sufficiently small momentum, we find sound modes with speed given by the conformal value and attenuation constant of hydrodynamic form. In particular we find sound at arbitrarily low T /μ, outside the usual hydrodynamic regime, but in the regime where a Fermi liquid exhibits Landau’s “zero” sound. In fact, the sound attenuation constant as a function of T /μ qualitatively resembles that of a Fermi liquid, including a maximum, which in a Fermi liquid signals the collisionless to hydrodynamic crossover. We also explore regimes of the tension and non-linearity parameter where two other proposed definitions of the crossover are viable, via pole collisions in Green’s functions or peak movement in the charge density spectral function. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum. We will argue, in particular, that in three spacetime dimensions the discrete spectra for the geometric boundary observables that we find in loop quantum gravity can be understood from the quantisation of a conformal boundary field theory in the continuum without ever introducing spin networks or triangulations of space. At a technical level, the starting point is the Hamiltonian formalism for general relativity in regions with boundaries at finite distance. At these finite boundaries, we choose specific conformal boundary conditions (the boundary is a minimal surface) that are derived from a boundary field theory for an SU(2) boundary spinor, which is minimally coupled to the spin connection in the bulk. The resulting boundary equations of motion define a conformal field theory with vanishing central charge. We will quantise this boundary field theory and show that the length of a one-dimensional cross section of the boundary has a discrete spectrum. In addition, we will introduce a new class of coherent states, study the quasi-local observables that generate the quasi-local Virasoro algebra and discuss some strategies to evaluate the partition function of the theory. [ABSTRACT FROM AUTHOR]

The bulk phase shift, related to a CFT four-point function, describes two-to-two scattering at fixed impact parameter in the dual AdS spacetime. We describe its properties for a generic CFT and then focus on large N CFTs with classical bulk duals. We compute the bulk phase shift for vector operators using Regge theory. We use causality and unitarity to put bounds on the bulk phase shift. The resulting constraints bound three-point functions of two vector operators and the stress tensor in terms of the gap o the theory. Similar bounds should hold for any spinning operator in a CFT. Holographically this implies that in a classical gravitational theory any non-minimal coupling to the graviton, as well as any other particle with spin greater than or equal to two, is suppressed by the mass of higher spin particles. [ABSTRACT FROM AUTHOR]

We consider states of holographic conformal field theories constructed by adding sources for local operators in the Euclidean path integral, with the aim of investigating the extent to which arbitrary bulk coherent states can be represented by such Euclidean path-integrals in the CFT. We construct the associated dual Lorentzian spacetimes perturbatively in the sources. Extending earlier work, we provide explicit formulae for the Lorentzian fields to first order in the sources for general scalar field and metric perturbations in arbitrary dimensions. We check the results by holographically computing the Lorentzian one-point functions for the sourced operators and comparing with a direct CFT calculation. We present evidence that at the linearized level, arbitrary bulk initial data profiles can be generated by an appropriate choice of Euclidean sources. However, in order to produce initial data that is very localized, the amplitude must be taken small at the same time otherwise the required sources diverge, invalidating the perturbative approach. [ABSTRACT FROM AUTHOR]