IIB supergravity and E10

TL;DR

This paper explores the connection between E10/K(E10) sigma-models and type IIB supergravity, showing that the sigma-model captures key supergravity features, including self-duality, through a level decomposition approach.

Contribution

It demonstrates a detailed correspondence between the E10 sigma-model and type IIB supergravity equations, including the self-duality condition, up to level four.

Findings

Sigma-model equations match supergravity equations up to level four.

Self-duality of the five-form field strength is derived from E10 symmetry.

The analysis uses a level decomposition aligned with the A8xA1 subalgebra.

Abstract

We analyse the geodesic E10/K(E10) sigma-model in a level decomposition w.r.t. the A8xA1 subalgebra of E10, adapted to the bosonic sector of type IIB supergravity, whose SL(2,R) symmetry is identified with the A1 factor. The bosonic supergravity equations of motion, when restricted to zeroth and first order spatial gradients, are shown to match with the sigma-model equations of motion up to level four. Remarkably, the self-duality of the five-form field strength is implied by E10 and the matching.