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We study maximally supersymmetric irrelevant deformations of the D1-D5 CFT that correspond to following the attractor flow in reverse in the dual half-BPS black string solutions of type IIB supergravity on K3. When a single, quadratic condition is imposed on the parameters of the 22 such irrelevant deformations, the asymptotics of the solution degenerate to a linear dilaton like spacetime. We identify each such degeneration limit with a known decoupling limit of string theory, which yields little string theory or deformations thereof (the so-called open brane LST, or ODp theories), compactified to two dimensions. This suggests that a 21-parameter family of the above deformations leads to UV-complete theories, which are string theories decoupled from gravity that are continuously connected to each other. All these theories have been argued to display Hagedorn behaviour; we show that including the F1 strings leads to an additional Cardy term. The resulting entropy formula closely resembles that of single-trace $T\bar T$-deformed CFTs, whose generalisations could provide possibly tractable effective two-dimensional descriptions of the above web of theories. We also consider the asymptotically flat black strings. At fixed temperature, the partition function is dominated by thermodynamically stable, small black string solutions, similar to the ones in the decoupled backgrounds. We show that certain asymptotic symmetries of these black strings bear a striking resemblance with the state-dependent symmetries of single-trace $T\bar T$, and break down precisely when the background solution reaches the large black string threshold. This suggests that small, asymptotically flat black strings may also admit a $T\bar T$ - like effective description., Comment: new in v2: important correction to the D1-D5 NCOS decoupling limit and related statements in section 4.2; an appendix added to discuss this limit pedagogically and more generally; another appendix supplemented with 10d formulae for the conserved charges necessary for this new discussion; references added and other minor modifications; main conclusions unchanged

We derive various properties of symmetric product orbifolds of $T\bar{T}$ and $J\bar{T}$ - deformed CFTs from a field-theoretical perspective. First, we generalise the known formula for the torus partition function of a symmetric orbifold theory in terms of the one of the seed to non-conformal two-dimensional QFTs; specialising this to seed $T\bar{T}$ and $J\bar{T}$ - deformed CFTs reproduces previous results in the literature. Second, we show that the single-trace $T\bar{T}$ and $J\bar{T}$ deformations preserve the Virasoro and Kac-Moody symmetries of the undeformed symmetric product orbifold CFT, including their fractional counterparts, as well as the KdV charges. Finally, we discuss correlation functions in these theories. By extending a previously-proposed basis of operators for $J\bar{T}$ - deformed CFTs to the single-trace case, we explicitly compute the correlation functions of both untwisted and twisted-sector operators and compare them to an appropriate set of holographic correlators. Our derivations are based mainly on Hilbert space techniques and completely avoid the use of conformal invariance, which is not present in these models., Comment: 50 pp, 5 figures

It has previously been proven that $T\bar T$ - deformed CFTs possess Virasoro $\times$ Virasoro symmetry at the full quantum level, whose generators are obtained by simply transporting the original CFT generators along the $T\bar T$ flow. In this article, we explicitly solve the corresponding flow equation in the classical limit, obtaining an infinite set of conserved charges whose action on phase space is well-defined even when the theory is on a compact space. The field-dependent coordinates that are characteristic of the $T\bar T$ deformation are shown to emerge unambiguously from the flow. Translating the symmetry transformations from the canonical to the covariant formalism, we find that they are different from those that have been previously proposed in the Lagrangian context, but that they agree precisely with those obtained from holography. We also comment on different possible bases for the symmetry generators and on how our explicit classical results could be extended perturbatively to the quantum level., Comment: 26 pages

We show that the three-dimensional asymptotically linear dilaton background that arises in the near-horizon decoupling region of NS5-branes compactified on $T^4$ admits boundary conditions that lead to an infinite set of symmetries. The associated conserved charges, which implement field-dependent coordinate transformations, are found to be identical to the corresponding generators in a symmetric product orbifold of $T\bar T$ - deformed CFTs. Their algebra is a non-linear modification of the $\mathrm{Virasoro \times Virasoro}$ algebra, which precisely coincides with the algebra of the "unrescaled" symmetry generators in $T\bar T$-deformed CFTs. This further strengthens a previously proposed link between the single-trace $T\bar T$ deformation and compactified little string theory., Comment: 31 + 19 pp

$J\bar T$-deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. They have been recently shown to possess an infinite set of symmetries, which are a continuous deformation of the Virasoro-Kac-Moody symmetries of the seed CFT. In this article, we put forth a definition of primary operators in $J\bar T$-deformed CFTs on a cylinder, which are singled out by having CFT-like momentum-space commutation relations with the symmetry generators in the decompatification limit. We show -- based on results we first derive for the case of $J^1 \wedge J^2$-deformed CFTs -- that all correlation functions of such operators in the $J\bar T$-deformed CFT can be computed exactly in terms of the correlation functions of the undeformed CFT and are crossing symmetric in the plane limit. In particular, two and three-point functions are simply given by the corresponding momentum-space correlator in the undeformed CFT, with all dimensions replaced by particular momentum-dependent conformal dimensions. Interestingly, scattering amplitudes off the near-horizon of extremal black holes are known to take a strikingly similar form., Comment: 30 pp

Various holographic set-ups in string theory suggest the existence of non-local, UV complete two-dimensional QFTs that possess Virasoro symmetry, in spite of their non-locality. We argue that $J\bar T$-deformed CFTs are the first concrete realisation of such "non-local CFTs", through a detailed analysis of their classical and quantum symmetry algebra. Classically, the symmetries consist of an infinite set of left-moving conformal and affine $U(1)$ transformations that generate a Witt-Kac-Moody algebra, as well as a set of non-local, field-dependent generalizations of right-moving conformal and affine $U(1)$ transformations, whose algebra depends on the chosen basis. Notably, there exists a basis, denoted as the "flowed" representation, in which the right-moving charge algebra is simply Witt-Kac-Moody. At the quantum level, we provide a concrete prescription for constructing the symmetry generators via a combination of the flow equations they satisfy and the Sugawara construction, and use this to explicitly resolve the ordering ambiguities and the quantum corrections to the generators up to second order in the $J\bar T$ coupling parameter. This construction naturally produces the "flowed" generators, whose algebra is Virasoro-Kac-Moody to all orders in the coupling, with the same central extension as that of the undeformed CFT. We use this input to work out the quantum modifications to the "unflowed" generator algebra. A peculiarity of the Virasoro generators we study is that their zero mode does not equal the Hamiltonian, but is a quadratic function of it; this helps reconcile the Virasoro symmetry with the non-locality of the model. We argue that also $T\bar T$-deformed CFTs posses Virasoro symmetry, and discuss the existence of such a symmetry in more general non-local QFTs., Comment: 34 pp

It has been recently shown that classical $J\bar T$ - deformed CFTs possess an infinite-dimensional Witt-Ka\v{c}-Moody symmetry, generated by certain field-dependent coordinate and gauge transformations. On a cylinder, however, the equal spacing of the descendants' energies predicted by such a symmetry algebra is inconsistent with the known finite-size spectrum of $J\bar T$ - deformed CFTs. Also, the associated quantum symmetry generators do not have a proper action on the Hilbert space. In this article, we resolve this tension by finding a new set of (classical) conserved charges, whose action is consistent with semi-classical quantization, and which are related to the previous symmetry generators by a type of energy-dependent spectral flow. The previous inconsistency between the algebra and the spectrum is resolved because the energy operator does not belong to the spectrally flowed sector., Comment: fixed a minus sign; various minor cosmetic changes; added a brief discussion

We show that $T \bar T, J \bar T$ and $J T_a$ - deformed classical CFTs possess an infinite set of symmetries that take the form of a field-dependent generalization of two-dimensional conformal transformations. If, in addition, the seed CFTs possess an affine $U(1)$ symmetry, we show that it also survives in the deformed theories, again in a field-dependent form. These symmetries can be understood as the infinitely-extended conformal and $U(1)$ symmetries of the underlying two-dimensional CFT, seen through the prism of the "dynamical coordinates" that characterise each of these deformations. We also compute the Poisson bracket algebra of the associated conserved charges, using the Hamiltonian formalism. In the case of the $J \bar T$ and $J T_a$ deformations, we find two copies of a functional Witt - Kac-Moody algebra. In the case of the $T \bar T$ deformation, we show that it is also possible to obtain two commuting copies of the Witt algebra., Comment: 28 + 12 pages, added some corrections and clarifications

We propose a general path-integral definition of two-dimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a $U(1)$ current. The deformed theory is obtained by coupling the original QFT to a flat dynamical gauge field and "half" a flat dynamical vielbein. The resulting partition function is shown to satisfy a geometric flow equation, which perfectly reproduces the flow equations for the deformed energy levels that were previously derived in the literature. The S-matrix of the deformed QFT differs from the original S-matrix only by an overall phase factor that depends on the charges and momenta of the external particles, thus supporting the conjecture that such QFTs are UV complete, although intrinsically non-local. For the special case of an integrable QFT, we check that this phase factor precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz equations., Comment: 21 pages, v2 signs fixed

We use the variational principle approach to derive the large $N$ holographic dictionary for two-dimensional $T\bar T$-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial "bulk cutoff" is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT., Comment: 23 + 5 pages, 4 figures

The $J\bar T$ deformation, built from the components of the stress tensor and of a $U(1)$ current, is a universal irrelevant deformation of two-dimensional CFTs that preserves the left-moving conformal symmetry, while breaking locality on the right-moving side. Operators in the $J\bar T$-deformed CFT are naturally labeled by the left-moving position and right-moving momentum and transform in representations of the one-dimensional extended conformal group. We derive an all-orders formula for the spectrum of conformal dimensions and charges of the deformed CFT, which we cross-check at leading order using conformal perturbation theory. We also compute the linear corrections to the one-dimensional OPE coefficients and comment on the extent to which the correlation functions in $J\bar T$-deformed CFTs can be obtained from field-dependent coordinate transformations., Comment: 26+7 pp

Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator $J \bar T$, where $J$ is a chiral $U(1)$ current and $\bar T$ is a component of the stress tensor. Assuming the original CFT was a holographic CFT, we work out the holographic dual of its $J \bar T$ deformation. We find that the dual spacetime is still AdS$_3$, but with modified boundary conditions that mix the metric and the Chern-Simons gauge field dual to the $U(1)$ current. We show that when the coefficient of the chiral anomaly for $J$ vanishes, the energy and thermodynamics of black holes obeying these modified boundary conditions precisely reproduce the previously derived field theory spectrum and thermodynamics. Our proposed holographic dictionary can also reproduce the field-theoretical spectrum in presence of the chiral anomaly, upon a certain assumption that we justify. The asymptotic symmetry group associated to these boundary conditions consists of two copies of the Virasoro and one copy of the $U(1)$ Ka\v{c}-Moody algebra, just as before the deformation; the only effect of the latter is to modify the spacetime dependence of the right-moving Virasoro generators, whose action becomes state-dependent and effectively non-local., Comment: v2: added discussion of the chiral anomaly and one appendix, affiliation and grant information updated

It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator $T \bar T$, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that posess a conserved $U(1)$ current, $J$. The deformation takes the schematic form $J \bar T$ and is interesting because it preserves an $SL(2,\mathbb{R}) \times U(1)$ subgroup of the original global conformal symmetries. For the case of a purely (anti)chiral current, we find the finite-size spectrum of the deformed theory and study its thermodynamic properties. We test our predictions in a simple example involving deformed free fermions., Comment: v3: institutional and grant information added

We study the null dipole deformation of N=4 super Yang-Mills theory, which is an example of a potentially solvable "dipole CFT": a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrodinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrodinger holography., Comment: 44 pages

Previous work has established an equality between the geodesic integral of a free bulk field in AdS and the contribution of the conformal descendants of its dual CFT primary operator to the OPE of two other operators inserted at the endpoints of the geodesic. Working in the context of the AdS$_3$/CFT$_2$ correspondence, we extend this relation to include the $1/N$ corrections to the bulk field obtained by dressing it with i) a $U(1)$ current and ii) the CFT stress tensor. In the former case, we argue that the contribution of the Ka\v{c}-Moody descendants to the respective boundary OPE equals the geodesic integral of a particular $U(1)$-dressed bulk field, which is framed to the boundary via a split Wilson line. In the latter case, we compute the gravitational $1/N$ corrections to the bulk field in various gauges, and then write a CFT expression for a putative bulk field whose geodesic integral captures the contribution of Virasoro descendants to the OPE of interest. We comment on the bulk interpretation of this expression., Comment: Added a detailed derivation of the bulk field in radial gauge, an appendix, references and various comments and cosmetic changes

We point out a simple relation between the bulk field at an arbitrary radial position and the boundary OPE, by placing some old work by Ferrara, Gatto, Grillo and Parisi in the AdS/CFT context. This gives us, in principle, a prescription for extracting the classical bulk field from the boundary conformal block, and also clarifies why the latter is computed by a geodesic Witten diagram. We apply this prescription to the BTZ black hole - viewed as a pure state created by the insertion of a heavy operator in the boundary CFT_2 - and use it to relate a classical field in the bulk to a heavy-light Virasoro conformal block in the boundary. In particular, we obtain a relation between the radial bulk position and the conformal ratios in the boundary CFT. We use this to show that the singular points of the radial bulk equation occur when the dual boundary operators approach each other and that the associated bulk monodromies map to monodromies of the (appropriately transformed) conformal block, thus providing a CFT interpretation of the radial monodromy., Comment: 30 pp, 3 figures

We revisit the holographic construction of (approximately) local bulk operators inside an eternal AdS black hole in terms of operators in the boundary CFTs. If the bulk operator carries charge, the construction must involve a qualitatively new object: a Wilson line that stretches between the two boundaries of the eternal black hole. This operator - more precisely, its zero mode - cannot be expressed in terms of the boundary currents and only exists in entangled states dual to two-sided geometries, which suggests that it is a state-dependent operator. We determine the action of the Wilson line on the relevant subspaces of the total Hilbert space, and show that it behaves as a local operator from the point of view of either CFT. For the case of three bulk dimensions, we give explicit expressions for the charged bulk field and the Wilson line. Furthermore, we show that when acting on the thermofield double state, the Wilson line may be extracted from a limit of certain standard CFT operator expressions. We also comment on the relationship between the Wilson line and previously discussed mirror operators in the eternal black hole., Comment: 44 pp

We explore the Papadodimas-Raju prescription for reconstructing the region behind the horizon of one-sided black holes in AdS/CFT in the case of the RP^2 geon - a simple, analytic example of a single-sided, asymptotically AdS_3 black hole, which corresponds to a pure CFT state that thermalises at late times. We show that in this specific example, the mirror operators involved in the reconstruction of the interior have a particularly simple form: the mirror of a single trace operator at late times is just the corresponding single trace operator at early times. We use some explicit examples to explore how changes in the state modify the geometry inside the horizon., Comment: 27+4 pages, 10 figures

We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS$_3$ solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS$_3$. Consequently, for each consistent choice of boundary conditions in AdS$_3$, we can define a consistent phase space in warped AdS$_3$ with identical conserved charges. This way, we easily obtain a Virasoro $\times$ Virasoro asymptotic symmetry algebra in warped AdS$_3$; two different types of Virasoro $\times$ Ka\v{c}-Moody symmetries are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro $\times$ Virasoro asymptotic symmetries can be extended to the entire (linearized) phase space. This implies that, at least at semi-classical level, consistent theories of gravity in warped AdS$_3$ are described by a two-dimensional conformal field theory, as long as stability is not an issue., Comment: 41 pages, 1 figure

Entanglement entropy obeys a 'first law', an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula $S=A/(4G_N)$, we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories., Comment: 41 pages

We propose a map for extracting the holographic meaning of the metric for a class of warped AdS_3 black strings in type IIB supergravity. Our choice of holographic data is based upon a general prescription due to Papadimitriou. With this choice, we find a holographic stress tensor that is both symmetric and conserved, at least when restricted to a particular sector of the theory. Using the holographic stress tensor, we compute the energy and momentum per unit length of the black strings, as well as the conformal anomaly, and we show that the results agree with those previously obtained via covariant methods., Comment: 20 pp

We use solution-generating techniques to construct interpolating geometries between general asymptotically flat, charged, rotating, non-extremal black holes in four and five dimensions and their subtracted geometries. In the four-dimensional case, this is achieved by the use of Harrison transformations, whereas in the five-dimensional case we use STU transformations. We also give the interpretation of these solution-generating transformations in terms of string (pseudo)-dualities, showing that they correspond to combinations of T-dualities and Melvin twists. Upon uplift to one dimension higher, these dualities allow us to "untwist" general black holes to AdS_3 times a sphere., Comment: 34 pages

Motivated by the desire to better understand finite-temperature holography for three-dimensional Schroedinger spacetimes, we: i) construct a four-parameter family of warped black string solutions of type IIB supergravity and ii) find the first consistent truncations of type IIB string theory to three dimensions that admit both supersymmetric Schroedinger solutions and warped generalizations of the BTZ black hole. Our analysis reveals a number of interesting features. One is that the thermodynamic properties of all the warped black strings, as well as the asymptotic symmetry group data, are identical to those of BTZ, in an appropriate parametrization. A more striking feature is that the spectrum of linearized perturbations around the various supersymmetric Schroedinger vacua oftentimes contains modes that carry energy flux through the spacetime boundary, which are usually believed to be unstable. A preliminary analysis indicates that, at least in the case of most interest, these modes do not lead to an instability., Comment: 36+20 pages, 5 figures

In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the bulk fields fluctuate. Recent work has used a Wilsonian framework to propose an alternative identification of the running couplings in terms of non-fluctuating data; in the classical limit, these new couplings do not satisfy the bulk equations of motion. We study renormalization scheme dependence in the latter formalism, and show that a scheme exists in which couplings to single trace operators realize particular solutions to the bulk equations of motion, in the semiclassical limit. This occurs for operators with dimension $\Delta \notin \frac{d}{2} + \ZZ$, for sufficiently low momenta. We then clarify the relation between the saddle point approximation to the Wilsonian effective action ($S_W$) and boundary conditions at a cutoff surface in AdS space. In particular, we interpret non-local multi-trace operators in $S_W$ as arising in Lorentzian AdS space from the temporary passage of excitations through the UV region that has been integrated out. Coarse-graining these operators makes the action effectively local., Comment: 30 pages including cover page and references, 3 figures. v2: References added

We show that the six-dimensional uplift of the five-dimensional Near-Horizon-Extremal-Kerr (NHEK) spacetime can be obtained from an AdS_3 X S^3 solution by a sequence of supergravity - but not string theory - dualities. We present three ways of viewing these pseudo-dualities: as a series of transformations in the STU model, as a combination of Melvin twists and T-dualities and, finally, as a sequence of two generalized spectral flows and a coordinate transformation. We then use these to find an infinite family of asymptotically flat embeddings of NHEK spacetimes in string theory, parameterized by the arbitrary values of the moduli at infinity. Our construction reveals the existence of non-perturbative deformations of asymptotically-NHEK spacetimes, which correspond to the bubbling of nontrivial cycles wrapped by flux, and paves the way for finding a microscopic field theory dual to NHEK which involves Melvin twists of the D1-D5 gauge theory. Our analysis also clarifies the meaning of the generalized spectral flow solution-generating techniques that have been recently employed in the literature., Comment: 53 pages, LaTeX

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 that the dual stress-energy tensor couples to the boundary metric of the auxiliary AdS(3) spacetime. The holographic stress tensor we obtain is symmetric, conserved and its trace yields the same conformal anomaly as in AdS(3)., Comment: 16 pp; minor corrections and references added

We study solutions of type IIB supergravity which are SL(2,R) x SU(2) x U(1)^2 invariant deformations of AdS_3 x S^3 x K3 and take the form of products of self-dual spacelike warped AdS_3 and a deformed three-sphere. One of these backgrounds has been recently argued to be relevant for a derivation of Kerr/CFT from string theory, whereas the remaining ones are holographic duals of two-dimensional dipole theories and their S-duals. We show that each of these backgrounds is holographically dual to a deformation of the DLCQ of the D1-D5 CFT by a specific supersymmetric (1,2) operator, which we write down explicitly in terms of twist operators at the free orbifold point. The deforming operator is argued to be exactly marginal with respect to the zero-dimensional nonrelativistic conformal (or Schroedinger) group - which is simply SL(2,R)_L x U(1)_R. Moreover, in the supergravity limit of large N and strong coupling, no other single-trace operators are turned on. We thus propose that the field theory duals to the backgrounds of interest are nonrelativistic CFTs defined by adding the single Schroedinger-invariant (1,2) operator mentioned above to the original CFT action. Our analysis indicates that the rotating extremal black holes we study are best thought of as finite right-moving temperature (non-supersymmetric) states in the above-defined supersymmetric nonrelativistic CFT and hints towards a more general connection between Kerr/CFT and two-dimensional non-relativistic CFTs., Comment: 48+8 pages, 4 figures; minor corrections and references added

Supersymmetric M/string compactifications to five dimensions contain BPS black string solutions with magnetic graviphoton charge P and near-horizon geometries which are quotients of AdS_3 x S^2. The holographic duals are typically known 2D CFTs with central charges c_L=c_R=6P^3 for large P. These same 5D compactifications also contain non-BPS but extreme Kerr-Newman black hole solutions with SU(2)_L spin J_L and electric graviphoton charge Q obeying Q^3 \leq J_L^2. It is shown that in the maximally charged limit Q^3 -> J_L^2, the near-horizon geometry coincides precisely with the right-moving temperature T_R=0 limit of the black string with magnetic charge P=J_L^{1/3}. The known dual of the latter is identified as the c_L=c_R=6J_L CFT predicted by the Kerr/CFT correspondence. Moreover, at linear order away from maximality, one finds a T_R \neq 0 quotient of the AdS_3 factor of the black string solution and the associated thermal CFT entropy reproduces the linearly sub-maximal Kerr-Newman entropy. Beyond linear order, for general Q^3

We discuss holography for Schrodinger solutions of both topologically massive gravity in three dimensions and massive vector theories in (d+1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (two dimensional in the case of TMG) deformed by certain operators that respect the Schrodinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions corresponds to operators that are labeled by their scaling dimension and the lightcone momentum k_v. We set up the holographic dictionary and compute 2-point functions of these operators both holographically and in field theory using conformal perturbation theory and find agreement. The counterterms needed for holographic renormalization are non-local in the v lightcone direction., Comment: 73 pages; v2: references added and minor improvements

We initiate a comprehensive study of a set of solutions of topologically massive gravity known as null warped anti-de Sitter spacetimes. These are pp-wave extensions of three-dimensional anti-de Sitter space. We first perform a careful analysis of the linearized stability of black holes in these spacetimes. We find two qualitatively different types of solutions to the linearized equations of motion: the first set has an exponential time dependence, the second - a polynomial time dependence. The solutions polynomial in time induce severe pathologies and moreover survive at the non-linear level. In order to make sense of these geometries, it is thus crucial to impose appropriate boundary conditions. We argue that there exists a consistent set of boundary conditions that allows us to reject the above pathological modes from the physical spectrum. The asymptotic symmetry group associated to these boundary conditions consists of a centrally-extended Virasoro algebra. Using this central charge we can account for the entropy of the black holes via Cardy's formula. Finally, we note that the black hole spectrum is chiral and prove a Birkoff theorem showing that there are no other stationary axisymmetric black holes with the specified asymptotics. We extend most of the analysis to a larger family of pp-wave black holes which are related to Schr\"odinger spacetimes with critical exponent z., Comment: 29 pages + appendices, refs added

AdS3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point \mu l=1. We study the possibility that the warped vacua of TMG, which exist for all values of \mu, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS3 vacua with Compere-Detournay boundary conditions are indeed stable in the range \mu l > 3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS3 vacuum. The situation somewhat resembles chiral gravity: although negative energy modes do exist, they are all excluded by the boundary conditions, and the perturbative spectrum solely consists of boundary (pure large gauge) gravitons., Comment: 30 pages, 1 figure

We explain why multi-centered black hole configurations where at least one of the centers is a large black hole do not contribute to the indexed degeneracies in theories with N=4 supersymmetry. This is a consequence of the fact that such configurations, although supersymmetric, belong to long supermultiplets. As a result, there is no entropy enigma in N=4 theories, unlike in N=2 theories., Comment: 14 pages

Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM^2) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c_L=12J / \hbar. This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T_L=1/2\pi and conjugate energy given by the zero mode generator, L_0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=2\pi J / \hbar for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c_L=12J / \hbar, and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c_L \sim 2 \times 10^{79}., Comment: 21 pages, no figures

These lectures give an introduction to the interrelated topics of Calabi-Yau compactification of the type II string, black hole attractors, the all-orders entropy formula, the dual (0,4) CFT, topological strings and the OSV conjecture. Based on notes by MG of lectures by AS at the 2006 Cargese summer school., Comment: 30 pp, 7 figures, based on lecture notes by A. Strominger at the 2006 Cargese summer school

A microscopic accounting of the entropy of a generic 5D supersymmetric rotating black hole, arising from wrapped M2-branes in Calabi-Yau compactified M-theory, is an outstanding unsolved problem. In this paper we consider an expansion around the zero-entropy, zero-temperature, maximally rotating ground state for which the angular momentum J_L and graviphoton charge Q are related by J_L^2=Q^3. At J_L=0 the near horizon geometry is AdS_2 x S^3. As J_L^2 goes to Q^3 it becomes a singular quotient of AdS_3 x S^2: more precisely, a quotient of the near horizon geometry of an M5 wrapped on a 4-cycle whose self-intersection is the 2-cycle associated to the wrapped-M2 black hole. The singularity of the AdS_3 quotient is identified as the usual one associated to the zero-temperature limit, suggesting that the (0,4) wrapped-M5 CFT is dual near maximality to the wrapped-M2 black hole. As evidence for this, the microscopic (0,4) CFT entropy and the macroscopic rotating black hole entropy are found to agree to leading order away from maximality., Comment: 10 pages, no figures

It is argued, using an M-theory lift, that the IIA partition function on a euclidean AdS_2 x S^2 x CY_3 attractor geometry computes the modified elliptic genus Z_BH of the associated black hole in a large charge expansion. The partition function is then evaluated using the Green-Schwarz formalism. After localizing the worldsheet path integral with the addition of an exact term, contributions arise only from the center of AdS_2 and the north and south poles of S^2. These are the toplogical and anti-topological string partition functions Z_top and {\bar Z_top} respectively. We thereby directly reproduce the perturbative relation Z_BH = |Z_top|^2., Comment: 19 pages, no figures

It is proposed that the quantum mechanics of N D4-branes and M D0-branes on the quintic is described by the dimensional reduction of a certain U(N)xU(M) quiver gauge theory, whose superpotential encodes the defining quintic polynomial. It is shown that the moduli space on the Higgs branch exactly reproduces the moduli space of degree N hypersurfaces in the quintic endowed with the appropriate line bundle, and that the cohomology growth reproduces the D4-D0 black hole entropy., Comment: 18 pages

We study higher-order corrections to two BPS solutions of 5D supergravity, namely the supersymmetric black ring and the spinning black hole. Due in part to our current relatively limited understanding of F-type terms in 5D supergravity, the nature of these corrections is less clear than that of their 4D cousins. Effects of certain $R^2$ terms found in Calabi-Yau compactification of M-theory are specifically considered. For the case of the black ring, for which the microscopic origin of the entropy is generally known, the corresponding higher order macroscopic correction to the entropy is found to match a microscopic correction, while for the spinning black hole the corrections are partially matched to those of a 4D $D0-D2-D6$ black hole., Comment: 9 pages

A surprising new seven-parameter supersymmetric black ring solution of five-dimensional supergravity has recently been discovered. In this paper, M-theory is used to give an exact microscopic accounting of its entropy., Comment: 5 pages; v2: References and acknowledgements added

We present an exact solution for a factorizable brane-world spacetime with two extra dimensions and explicit brane sources. The compactification manifold has the topology of a two-sphere, and is stabilized by a bulk cosmological constant and magnetic flux. The geometry of the sphere is locally round except for conical singularities at the locations of two antipodal branes, deforming the sphere into an American-style football. The bulk magnetic flux needs to be fine-tuned to obtain flat geometry on the branes. Once this is done, the brane geometry is insensitive to the brane vacuum energy, which only affects the conical deficit angle of the extra dimensions. Solutions of this form provide a new arena in which to explore brane-world phenomenology and the effects of extra dimensions on the cosmological constant problem.