Pure and Twisted Holography

TL;DR

This paper explores a topologically twisted holographic duality between a boundary N=2 supersymmetric Liouville conformal field theory and a bulk three-dimensional supergravity, establishing a metric-independent topological AdS/CFT correspondence.

Contribution

It introduces a topologically twisted version of the holographic duality involving N=2 Liouville theory and 3D supergravity, with explicit calculations supporting the duality.

Findings

Bulk supergravity configurations match boundary chiral ring structure constants.

The duality is independent of the boundary metric, confirming topological nature.

Quantization of solutions supports the holographic correspondence.

Abstract

We analyse a simple example of a holographically dual pair in which we topologically twist both theories. The holography is based on the two-dimensional N=2 supersymmetric Liouville conformal field theory that defines a unitary bulk quantum supergravity theory in three-dimensional anti-de Sitter space. The supersymmetric version of three-dimensional Liouville quantum gravity allows for a topological twist on the boundary and in the bulk. We define the topological bulk supergravity theory in terms of twisted boundary conditions. We corroborate the duality by calculating the chiral configurations in the bulk supergravity theory and by quantising the solution space. Moreover, we note that the boundary calculation of the structure constants of the chiral ring carries over to the bulk theory as well. We thus construct a topological AdS/CFT duality in which the bulk theory is independent of the boundary metric.