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The Chern-Simons formulation of $AdS_3$ supergravity is considered. Asymptotic conditions on the Rarita-Schwinger fields are given. Together with the known boundary conditions on the bosonic fields, these ensure that the asymptotic algebra…
We consider three-dimensional Einstein gravity in Euclidean signature with a finite boundary of torus topology endowed with an induced metric of fixed conformal class and a constant trace of extrinsic curvature $K$. For vanishing, positive,…
We revisit some properties of AdS$_2$ Einstein-Maxwell gravity with the aim of reconciling apparently conflicting results in prior literature. We show that the two dimensional theory can be obtained as a dimensional reduction of the three…
Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. This is because (i) Chern-Simons theory with a gauge group $SL(2,R) \times SL(2,R)$ on a space-time…
We consider bosonic strings propagating on Euclidean adS_3, and study in particular the realization of various worldsheet symmetries. We give a proper definition for the Brown-Henneaux asymptotic target space symmetry, when acting on the…
We study asymptotic symmetry algebras for classes of three dimensional supergravities with and without cosmological constant. In the first part we generalise some of the non-Dirichlet boundary conditions of $AdS_3$ gravity to extended…
The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and postulating that the horizon area must be proportional…
We construct a two-dimensional dual field theory induced at the boundary of three-dimensional Chern-Simons gravity invariant under the Maxwell algebra. The resulting action takes the form of a Maxwellian extension of the flat Liouville…
This thesis is organized as follows. In Chapter 2, some preliminaries are given on isometries and conformal symmetries, and we become familiar with the Virasoro algebra. Two examples of classical central charges are discussed. Chapter 3…
A generalization of the Brown-Henneaux boundary conditions is introduced for pure gravity with negative cosmological constant in 3 dimensions. This leads to new degrees of freedom and to an enhancement of the symmetry algebra. Up to the…
We investigate new boundary conditions in three-dimensional asymptotically Anti-de Sitter gravity coupled to higher-spin fields, allowing for arbitrary boundary degrees of freedom. This generalization gives rise to an enlarged algebra of…
It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer $k$. Gravitational excitations are then described by…
We study the conditions of integrability when the boundary terms are considered in the variation of the geometric contribution of the Einstein-Hilbert action. We explore the emergent physical dynamics that is obtained when we make a…
In this work we explore ideas in quantizing AdS$_3$ Einstein gravity. We start with the most general solution to the 3d gravity theory which respects Brown-Henneaux boundary conditions. These solutions are specified by two holomorphic…
We investigate systematically the asymptotic dynamics and symmetries of all three-dimensional extended AdS supergravity models. First, starting from the Chern-Simons formulation, we show explicitly that the (super)anti-de Sitter boundary…
Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by $G$ and $\Lambda$. As a consequence, correlation functions of the boundary stress tensor in AdS$_3$ are uniquely fixed in terms of one…
In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory.…
A finite action principle for Einstein-Gauss-Bonnet AdS gravity is presented. The boundary term, which is different for even and odd dimensions, is a functional of the boundary metric, intrinsic curvature and extrinsic curvature. For even…
We revisit the description of the space of asymptotically AdS3 solutions of pure gravity in three dimensions with a negative cosmological constant as a collection of coadjoint orbits of the Virasoro group. Each orbit corresponds to a set of…
We propose novel asymptotically locally flat boundary conditions for Einstein Gravity without cosmological constant in four dimensions that are consistent with the variational principle. They allow for complex solutions that are…