Twisted supergravity and its quantization

TL;DR

This paper proposes conjectural descriptions of twisted supergravity theories in 10 dimensions using topological string theories, providing evidence for their properties and quantization, especially for type IIB supergravity.

Contribution

It introduces conjectural models of twisted supergravity in 10 dimensions via topological string theories and demonstrates their potential for unique perturbative quantization.

Findings

Candidate twisted supergravity theories contain expected residual supersymmetry.

The type IIB twisted supergravity admits a unique perturbative quantization.

Open string theories on branes are shown to be twists of maximally supersymmetric gauge theories.

Abstract

Twisted supergravity is supergravity in a background where the bosonic ghost field takes a non-zero value. This is the supergravity counterpart of the familiar concept of twisting supersymmetric field theories. In this paper, we give conjectural descriptions of type IIA and IIB supergravity in $10$ dimensions. Our conjectural descriptions are in terms of the closed-string field theories associated to certain topological string theories, and we conjecture that these topological string theories are twists of the physical string theories. For type IIB, the results of arXiv:1505.6703 show that our candidate twisted supergravity theory admits a unique quantization in perturbation theory. This is despite the fact that the theories, like the original physical theories, are non-renormalizable. Although we do not prove our conjectures, we amass considerable evidence. We find that our candidates for the twisted supergravity theories contain the residual supersymmetry one would expect. We also prove (using heavily a result of Baulieu arXiv:1009.3893) the open string version of our conjecture: the theory living on a brane in the topological string theory is a twist of the maximally supersymmetric gauge theory living on the brane in the physical string theory.