Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4

TL;DR

This paper explores the rich symmetry structures of pure N=2 supergravity in four dimensions, revealing connections to Kac-Moody algebras and their implications for BPS brane solutions.

Contribution

It demonstrates the presence of an underlying Lorentzian Kac-Moody algebra SU(2,1)^{+++} in N=2 supergravity and links it to known algebraic structures like e_{11}.

Findings

SU(2,1) symmetry acts on BPS branes.

Evidence for SU(2,1)^{+++} as underlying algebra.

Embedding of SU(2,1)^{+++} in e_{11} via brane physics.

Abstract

We study the symmetries of pure N=2 supergravity in D=4. As is known, this theory reduced on one Killing vector is characterised by a non-linearly realised symmetry SU(2,1) which is a non-split real form of SL(3,C). We consider the BPS brane solutions of the theory preserving half of the supersymmetry and the action of SU(2,1) on them. Furthermore we provide evidence that the theory exhibits an underlying algebraic structure described by the Lorentzian Kac-Moody group SU(2,1)^{+++}. This evidence arises both from the correspondence between the bosonic space-time fields of N=2 supergravity in D=4 and a one-parameter sigma-model based on the hyperbolic group SU(2,1)^{++}, as well as from the fact that the structure of BPS brane solutions is neatly encoded in SU(2,1)^{+++}. As a nice by-product of our analysis, we obtain a regular embedding of the Kac-Moody algebra su(2,1)^{+++} in e_{11} based on brane physics.