Conformal blocks for AdS5 singletons

TL;DR

This paper derives conformal blocks for the singleton sector in certain IIB string theory compactifications, showing they match the boundary U(1) gauge theory partition function and exploring duality symmetries.

Contribution

It provides a non-topological derivation of conformal blocks for IIB string theory's singleton sector, including second-derivative terms, and connects them to boundary gauge theory and dualities.

Findings

Conformal blocks match the boundary U(1) gauge theory partition function.

Reproduction of magnetic translation and SL(2,Z) S-duality actions.

Identification of subtleties in IIB Chern-Simons phase normalization.

Abstract

We give a simple derivation of the conformal blocks of the singleton sector of compactifications of IIB string theory on spacetimes of the form X5 x Y5 with Y5 compact, while X5 has as conformal boundary an arbitrary 4-manifold M4. We retain the second-derivative terms in the action for the B,C fields and thus the analysis is not purely topological. The unit-normalized conformal blocks agree exactly with the quantum partition function of the U(1) gauge theory on the conformal boundary. We reproduce the action of the magnetic translation group and the SL(2,Z) S-duality group obtained from the purely topological analysis of Witten. An interesting subtlety in the normalization of the IIB Chern-Simons phase is noted.