Anti–de Sitter holography for gravity and higher spin theories in two dimensions

Abstract

We provide a holographic description of two-dimensional dilaton gravity with Anti-de Sitter boundary conditions. We find that the asymptotic symmetry algebra consists of a single copy of the Virasoro algebra with non-vanishing central charge and point out difficulties with the standard canonical treatment. We generalize our results to higher spin theories and thus provide the first examples of two-dimensional higher spin gravity with holographic description. For spin-3 gravity we find that the asymptotic symmetry algebra is a single copy of the W3-algebra.

Most general AdS3 boundary conditions

“…Moreover, it could be rewarding to consider generalizations to other dimensions. For instance, it is conceivable that the AdS 2 bc's proposed in [50,51] can be generalized along the lines of our present work and may lead to a single copy of an sl(2) k current algebra as ASA. (For a relation between AdS 3 and AdS 2 gravity see [52].)…”

Menagerie of AdS2 boundary conditions

“…The asymptotic symmetries for these boundary conditions were previously analyzed in [69,72]. It was shown therein that the charges associated with these asymptotic symmetries are, in general, non-integrable.…”

“…To the best of our knowledge, the first holographic approach allowing for a fluctuating dilaton at the boundary was [72]. However, in that paper a well-defined variational principle was only achieved in the presence of a disconnected boundary (i.e., global AdS 2 with topology of a strip) so that non-vanishing variations from one boundary component are cancelled by a similar contribution, but with opposite sign, from the other boundary component.…”

“…We will now turn to the set of stricter boundary conditions that was analyzed previously in [69,72] and that is more "typical" for asymptotically AdS 2 behavior since the leading order metric is not allowed to fluctuate. Setting L 0 = 0 and fixing L + to the convenient constant value L + = 1/2, metric and dilaton read…”

Models of AdS2 backreaction and holography

“…Previous investigations of AdS 2 holography [23][24][25][26][27] have studied either propagating fields or the gravitational sector separately, whereas we are interested in the coupling between the two. We continue to Euclidean coordinates; the fields remain real.…”