Exceptional geometry and tensor fields

TL;DR

This paper develops a tensor calculus framework for exceptional generalised geometry, providing unified expressions for connections, torsion, and curvature across various exceptional groups, and explores tensor gauge fields coupled to this geometry.

Contribution

It introduces a unified tensor calculus for exceptional generalised geometry and extends it to include tensor gauge fields, advancing the mathematical tools for this field.

Findings

Unified formulation of connections, torsion, and curvature for E_n(n) groups

Extension of tensor calculus to tensor gauge fields in exceptional geometry

Properties of forms on manifolds are generalized to these tensor fields

Abstract

We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to the exceptional generalised gravity. Many of the properties of forms on manifolds are carried over to these fields.