AdS2 Quantum Gravity and String Theory

TL;DR

This paper explores the enhanced conformal symmetry in AdS2 quantum gravity, investigates scalar fields and string theories in this setting, and proposes a connection between AdS2 and AdS3 Virasoro algebras.

Contribution

It demonstrates the enlargement of the isometry group to the full conformal group in AdS2 and links AdS2 string theories to the near-horizon limit of AdS3 string theories.

Findings

Massive scalars have conformal weights shifted by their mass.

Boundary operators are derived as derivatives of scalar fields for integral weights.

Evidence suggests a topological twist relates AdS2 and AdS3 Virasoro algebras.

Abstract

AdS2 has an SL(2,R) isometry group. It is argued that in the context of quantum gravity on AdS2 this group is enlarged to the full infinite-dimensional 1+1 conformal group. Massive scalar fields are coupled to AdS2 gravity and shown to have associated conformal weights h(m) shifted by their mass. For integral values of h primary boundary operators are obtained as h normal derivatives of the scalar field. AdS2 string theories arise in the `very-near-horizon' limit of S1-compactified AdS3 string theories. This limit corresponds to energies far below the compactification scale. The dual conformal field theory has one null dimension and can in certain cases be described as the discrete light cone quantization of a two-dimensional deformed symmetric-product conformal field theory. Evidence is given that the AdS2 Virasoro algebra is related to the right-moving AdS3 Virasoro algebra by a topological twist which shifts the central charge to zero.