We perform the Hamiltonian reduction of Lower Spin Gravity, the simplest bulk dual for a Warped Conformal Field Theory (WCFT), consisting in an SL(2) × U(1) Chern-Simons model. We identify the boundary action as the geometric action on coadjoint orbits of the Warped Virasoro group. We use this reduced action to compute one-loop contributions to the torus partition function and compare them to the Warped Virasoro characters.

Belgium

Stéphane Detournay

Quentin Vandermiers

Geometric actions for Lower Spin Gravity

In the context of warped conformal field theories (WCFT), the derivation of the warped Cardy formula relies on the zero mode spectrum being bounded from below. Generically, this is not true for holographic WCFTs in “canonical” ensemble, whereas this condition is satisfied in the “quadratic” ensemble, making it more natural in holographic setups. In this work, we find a new set of boundary conditions in three-dimensional Topologically Massive Gravity (TMG) such that the putative dual theory is a WCFT in quadratic ensemble. Surprisingly, imposing the equations of motion, we obtain a closed form metric spanned by two arbitrary chiral functions, analogous to the Bañados metrics in Einstein gravity. Surface charges for these boundary conditions are not a priori integrable and we discuss two choices of boundary conditions to make them so. We obtain the bulk thermodynamic entropy of warped BTZ black holes by making use of the warped Cardy formula, in its regime of validity. We also discuss the issue of identifying the vacuum in our solution space: demanding the enhancement of global symmetries selects only a family of solutions, out of which the unique vacuum must be carefully singled out.

Netherlands

Ankit Aggarwal

Luca Ciambelli

Antoine Somerhausen

Boundary conditions for warped AdS3 in quadratic ensemble

The phase space of three-dimensional gravity with Compere-Song-Strominger (CSS) boundary conditions is endowed with asymptotic symmetries consisting in the semidirect product of a Virasoro and a <math><mover><mi>u</mi><mo>^</mo></mover><mo>(</mo><mn>1</mn><mo>)</mo></math> Kač-Moody algebra, and contains Bañados-Teitelboim-Zanelli (BTZ) black holes whose entropy can be accounted for by the degeneracy of states of a warped Conformal Field Theory (CFT). By embedding these boundary conditions in topologically massive gravity, we observe the existence of two special points in the space of couplings parametrized by the <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> radius <math><mo>ℓ</mo></math> and the Chern-Simons coupling <math><mi>μ</mi></math>. When <math><mi>μ</mi><mo>=</mo><mo>±</mo><mfrac><mn>1</mn><mo>ℓ</mo></mfrac></math>, the asymptotic symmetries reduce to either a chiral Virasoro algebra or a pure <math><mover><mi>u</mi><mo>^</mo></mover><mo>(</mo><mn>1</mn><mo>)</mo></math> Kač-Moody current algebra. At those points, black holes have positive energy while that of linearized excitations are non-negative.

New chiral gravity

We study warped flat geometries in three-dimensional topologically massive gravity. They are quotients of global warped flat spacetime, whose isometries are given by the 2-dimensional centrally extended Poincaré algebra. The latter can be obtained as a certain scaling limit of Warped AdS3 space with a positive cosmological constant. We discuss the causal structure of the resulting spacetimes using projection diagrams. We study their charges and thermodynamics, together with asymptotic Killing vectors preserving a consistent set of boundary conditions including them. The asymptotic symmetry group is given by a Warped CFT algebra, with a vanishing current level. A generalization of the derivation of the Warped CFT Cardy formula applies in this case, reproducing the entropy of the warped flat cosmological spacetimes.

Wout Merbis

Ireland

Gim Ng

Austria

Raphaela Wutte

Warped flatland

We study the relationship between TsT transformations, marginal deformations of string theory on AdS backgrounds, and irrelevant deformations of 2d CFTs. We show that TsT transformations of NS-NS backgrounds correspond to instantaneous deformations of the worldsheet action by the antisymmetric product of two Noether currents, holographically mirroring the definition of the $$ T\overline{T},J\overline{T},T\overline{J} $$ , and $$ J\overline{J} $$ deformations of 2d CFTs. Applying a TsT transformation to string theory on BTZ × × we obtain a general class of rotating black string solutions, including the Horne-Horowitz and the Giveon-Itzhaki-Kutasov ones as special cases, which we show are holographically dual to thermal states in single-trace $$ T\overline{T} $$ -deformed CFTs. We also find a smooth solution interpolating between global AdS in the IR and a linear dilaton background in the UV that is interpreted as the NS-NS ground state in the dual $$ T\overline{T} $$ -deformed CFT. This background suggests the existence of an upper bound on the deformation parameter above which the solution becomes complex. We find that the worldsheet spectrum, the thermodynamics of the black strings (in particular their Bekenstein-Hawking entropy), and the critical value of the deformation parameter match the corresponding quantities obtained from single-trace $$ T\overline{T} $$ deformations.

China

Luis Apolo

United States

Wei Song

TsT,

We propose a set of diffeomorphism that act non-trivially near the horizon of the Kerr black hole. We follow the recent developments of Haco-Hawking-Perry-Strominger to quantify this phase space, with the most substantial difference being our choice of vectors fields. Our gravitational charges are organized into a Virasoro-Kac-Moody algebra with non-trivial central extensions. We interpret this algebra as arising from a warped conformal field theory. Using the data we can infer from this warped CFT description, we capture the thermodynamic properties of the Kerr black hole.

Alejandra Castro

Warped symmetries of the Kerr black hole

We determine a consistent phase space for a theory consisting in the Einstein-Hilbert action coupled to matter fields (dilaton, one-form, two-form) and containing three-dimensional black strings (the Horne-Horowitz solution and generalizations thereof). The theory at hand is the low energy effective action for the bosonic sector of heterotic string theory. We find a consistent set of boundary conditions whose algebra of asymptotic charges consist in a single Virasoro algebra supplemented by three global u(1) generators. We also discuss the thermodynamics of the zero-mode solutions and point out some peculiar features of this system.

France

P. Petropoulos

Céline Zwikel

Asymptotic symmetries of three-dimensional black strings

We provide a simple holographic description for a warped conformal field theory (WCFT) at finite temperature. To this end, we study the counterpart of warped anti–de Sitter black holes in three dimensions using a lower-spin <math><mrow><mi>sl</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo><mo>⊕</mo><mi>u</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> Chern-Simons theory proposed by Hofman and Rollier. We determine the asymptotic symmetries, thermal entropy and holographic entanglement entropy and show that all these quantities are in perfect agreement with the expectations from the dual WCFT perspective. In addition, we provide a metric interpretation of our results which naturally fits with our analysis in the Chern-Simons formulation.

Tatsuo Azeyanagi

Max Riegler

Warped black holes in lower-spin gravity

In this paper we investigate spectral flow symmetry in asymptotically flat spacetimes both from a gravity as well as a putative dual quantum field theory perspective. On the gravity side we consider models in Einstein gravity and supergravity as well as their "reloaded" versions, present suitable boundary conditions, determine the respective asymptotic symmetry algebras and the thermal entropy of cosmological solutions in each of these models. On the quantum field theory side we identify the spectral flow symmetry as automorphisms of the underlying symmetry algebra of the theory. Using spectral flow invariance we then determine the thermal entropy of these quantum field theories and find perfect agreement with the results from the gravity side. In addition we determine logarithmic corrections to the thermal entropy.

India

Rudranil Basu

Spectral flow in 3D flat spacetimes

We consider warped AdS 3 black holes in generic higher derivatives gravity theories in 2+1 dimensions. The asymptotic symmetry group of the phase space containing these black holes is the semi-direct product of a centrally extended Virasoro algebra and an affine u (1) Kac-Moody algebra. Previous works have shown that in some specific theories, the entropy of these black holes agrees with a Cardy-like entropy formula derived for warped conformal field theories. In this paper, we show that this entropy matching continues to hold for the most general higher derivative theories of gravity. We also discuss the existence of phase transitions.