Gauged D = 9 supergravities and Scherk–Schwarz reduction

Abstract

Generalized 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, and there are three distinct gauged supergravities that result, corresponding to monodromies in the three conjugacy classes of . There is one gauging of the compact SO(2) subgroup of the and two distinct gaugings of non-compact SO(1, 1) subgroups, embedded differently in . 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 , and the distinct theories correspond to conjugacy classes. The theories consist of two infinite classes with quantized 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.