Gauged D=9 Supergravities and Scherk-Schwarz Reduction

TL;DR

This paper classifies gauged supergravities obtained from Scherk-Schwarz reductions of IIB supergravity on a circle, focusing on the role of SL(2,R) monodromies and their conjugacy classes, including quantized and sporadic theories.

Contribution

It provides a detailed classification of gauged supergravities arising from circle reductions with SL(2,R) monodromies, including new insights into conjugacy classes and quantized parameters.

Findings

Three distinct gauged supergravities from SL(2,R) monodromies.

Quantized mass parameters m=1,2,3,... for certain theories.

Identification of sporadic theories linked to hyperbolic conjugacy classes.

Abstract

Generalised Scherk-Schwarz reductions in which compactification on a circle is accompanied by a twist with an element of a global symmetry G typically lead to gauged supergravities and are classified by the monodromy matrices, up to conjugation by the global symmetry. For compactifications of IIB supergravity on a circle, G=SL(2,R) and there are three distinct gauged supergravities that result, corresponding to monodromies in the three conjugacy classes of SL(2,R). There is one gauging of the compact SO(2) subgroup of the SL(2,R) and two distinct gaugings of non-compact SO(1,1) subgroups, embedded differently in SL(2,R). The non-compact gaugings can be obtained from the compact one via an analytic continuation of the kind used in D=4 gauged supergravities. For the superstring, the monodromy must be in SL(2,Z), and the distinct theories correspond to SL(2,Z) conjugacy classes. The theories consist of two infinite classes with quantised mass parameter m=1,2,3,..., three exceptional theories corresponding to elliptic conjugacy classes, and a set of sporadic theories corresponding to hyperbolic conjugacy classes.