We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and W 3 higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions. We show that the reduction gives two copies of chiral bosons on the boundary. In particular, we take into account the holonomy of the Chern-Simons connection which manifests itself as zero mode of the momentum of the boundary chiral boson. We provide an equivalent formulation of the boundary action which we claim to be the geometric action on symplectic leaves of a (super-)Virasoro or a higher spin W  N  Poisson manifold in the case of supergravity or higher spin gravity respectively, where the intersection of leaves (given in terms of leaves representatives) can be identified as the bulk holonomy. This concludes the extension to non-linear algebras where the notion of coadjoint representation is not well-defined. The boundary Hamiltonian depends on a choice of boundary conditions and is equivalent to the Schwarzian action for corresponding Brown-Henneaux boundary conditions. We make this connection explicit in the extended supersymmetric case. Moreover, we discuss the geometric action in the case of W 3 AdS3 gravity in both   <math> <mi>sl</mi> </math>  $$ \mathfrak{sl} $$ (3) highest weight representations based on principal and diagonal   <math> <mi>sl</mi> </math>  $$ \mathfrak{sl} $$ (2) embeddings.

Netherlands

Wout Merbis

Chile

Turmoli Neogi

Croatia

Arash Ranjbar

Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited

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.

Belgium

Stéphane Detournay

Ireland

Gim Ng

Austria

Raphaela Wutte

Warped flatland

The asymptotic dynamics of AdS3 gravity with two asymptotically anti-de Sitter regions is investigated, paying due attention to the zero modes, i.e., holonomies along non-contractible circles and their canonically conjugates. This situation covers the eternal black hole solution. We derive how the holonomies around the non-contractible circles couple the fields on the two different boundaries and show that their canonically conjugate variables, needed for a consistent dynamical description of the holonomies, can be related to Wilson lines joining the boundaries. The action reduces to the sum of four free chiral actions, one for each boundary and each chirality, with additional non-trivial couplings to the zero modes which are explicitly written. While the Gauss decomposition of the SL(2, ℝ) group elements is useful in order to treat hyperbolic holonomies, the Iwasawa decomposition turns out to be more convenient in order to deal with elliptic and parabolic holonomies. The connection with the geometric action is also made explicit. Although our paper deals with the specific example of two asymptotically anti-de Sitter regions, most of our global considerations on holonomies and radial Wilson lines qualitatively apply whenever there are multiple boundaries, independently of the form that the boundary conditions explicitly take there.

France

Marc Henneaux

Asymptotic dynamics of AdS3 gravity with two asymptotic regions

In this paper we perform the Hamiltonian reduction of the action for three- dimensional Einstein gravity with vanishing cosmological constant using the Chern-Simons formulation and Bondi-van der Burg-Metzner-Sachs (BMS) boundary conditions. An equivalent formulation of the boundary action is the geometric action on BMS3 coad- joint orbits, where the orbit representative is identified as the bulk holonomy. We use this reduced action to compute one-loop contributions to the torus partition function of all BMS3 descendants of Minkowski spacetime and cosmological solutions in flat space. We then consider Wilson lines in the ISO(2, 1) Chern-Simons theory with endpoints on the boundary, whose reduction to the boundary theory gives a bilocal operator. We use the expectation values and two-point correlation functions of these bilocal operators to compute quantum contributions to the entanglement entropy of a single interval for BMS3 invariant field theories and BMS3 blocks, respectively. While semi-classically the BMS3 boundary theory has central charges c 1 = 0 and c 2 = 3/G  N , we find that quantum corrections in flat space do not renormalize G  N , but rather lead to a non-zero c 1.

United States

Max Riegler

Geometric actions and flat space holography

We set up the bootstrap procedure for supersymmetric Galilean Conformal (SGC) field theories in two dimensions by constructing the SGC blocks in the  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ and two possible  <math><mi>N</mi><mo>=</mo><mn>2</mn></math> $$ \mathcal{N}=2 $$ extensions of the Galilean conformal algebra. In all analyzed cases, we present the bootstrap equations by crossing symmetry of the four point function. In addition, we compute the global SGC blocks analytically by solving the differential equations obtained by acting with the Casimirs of the global subalgebras inside the four point function. These global blocks agree with the general SGC blocks in the limit of large central charge. We comment on possible applications to supersymmetric BMS3 invariant field theories and flat holography.

China

Ivano Lodato

India

 Zodinmawia

Supersymmetric Galilean conformal blocks

We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u $$ \mathfrak{u} $$ (1) current algebras and recover the surprisingly simple entropy formula S  = 2 π ( J 0 +  +  J 0 − ), where J 0 ± are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.

Daniel Grumiller

Philip Hacker

Soft hairy warped black hole entropy

We consider two possible flat space limits of three dimensional N = 1 , 1 $$ \mathcal{N}=\left(1,\ 1\right) $$ AdS supergravity. They differ by how the supercharges are scaled with the AdS radius ℓ : the first limit (democratic) leads to the usual super-Poincaré theory, while a novel ‘twisted’ theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non- and ultra-relativistic limits of the N = 1 , 1 $$ \mathcal{N}=\left(1,\ 1\right) $$ Virasoro algebra in two dimensions. Finally, we study the supersymmetric energy bounds and find the explicit form of the asymptotic and global Killing spinors of supersymmetric solutions in both flat space supergravity theories.

Super-BMS 3 algebras from N = 2 $$ \mathcal{N}=2 $$ flat supergravities

Using the frame formulation of multi-gravity in three dimensions, we show that demanding the presence of secondary constraints which remove the Boulware-Deser ghosts restricts the possible interaction terms of the theory and identifies invertible frame field combinations whose effective metric may consistently couple to matter. The resulting ghost-free theories can be represented by theory graphs which are trees. In the case of three frame fields, we explicitly show that the requirement of positive masses and energies for the bulk spin-2 modes in AdS 3 is consistent with a positive central charge for the putative dual CFT 2 .

Hamid Afshar

Eric Bergshoeff

Interacting spin-2 fields in three dimensions

Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories are free of scalar ghosts. We canonically analyze these theories and construct the gauge generators and the boundary central charges. The models we construct are all consistent with a holographic c -theorem which, however, does not imply that they are unitary. We find that Born-Infeld gravity in three dimensions is contained within these models as a subclass.

Hamid R. Afshar

Eric A. Bergshoeff

Extended massive gravity in three dimensions

We show that the parameter space of Zwei-Dreibein Gravity (ZDG) in AdS 3 exhibits critical points, where massive graviton modes coincide with pure gauge modes and new ‘logarithmic’ modes appear, similar to what happens in New Massive Gravity. The existence of critical points is shown both at the linearized level, as well as by finding AdS wave solutions of the full non-linear theory, that behave as logarithmic modes towards the AdS boundary. In order to find these solutions explicitly, we give a reformulation of ZDG in terms of a single Dreibein, that involves an infinite number of derivatives. At the critical points, ZDG can be conjectured to be dual to a logarithmic conformal field theory with zero central charges, characterized by new anomalies whose conjectured values are calculated.