E7(7) formulation of N=2 backgrounds

TL;DR

This paper reformulates N=2 supergravity backgrounds in type II string theory using E7(7) symmetry, unifying various scalar fields and potentials within an extended geometric framework.

Contribution

It introduces an E7(7)-invariant formalism for N=2 backgrounds, combining NS and RR sectors into a unified geometric description and deriving explicit expressions for moduli space potentials.

Findings

E7(7)-invariant Kahler and hyperkahler potentials derived

Unified description of NS and RR scalar fields in extended geometry

Explicit E7(7) expressions for scalar potentials and vacua equations

Abstract

In this paper we reformulate N=2 supergravity backgrounds arising in type II string theory in terms of quantities transforming under the U-duality group E7(7). In particular we combine the Ramond--Ramond scalar degrees of freedom together with the O(6,6) pure spinors which govern the Neveu-Schwarz sector by considering an extended version of generalised geometry. We give E7(7)-invariant expressions for the Kahler and hyperkahler potentials describing the moduli space of vector and hypermultiplets, demonstrating that both correspond to standard E7(7) coset spaces. We also find E7(7) expressions for the Killing prepotentials defining the scalar potential, and discuss the equations governing N=1 vacua in this formalism.