E_{7(7)} symmetry and dual gauge algebra of M-theory on a twisted seven-torus

TL;DR

This paper explores the dual gauge algebra structure in M-theory compactified on a twisted 7-torus, revealing how fluxes and gaugings relate to the E_{7(7)} symmetry and dual vector fields after dualization.

Contribution

It uncovers the dual gauge algebra within E_{7(7)} in M-theory compactifications, highlighting the role of dual vector fields and the impact of fluxes and gaugings.

Findings

Dual gauge algebra is a subalgebra of E_{7(7)}.

Dual vector fields are associated with the original vector fields involved in the Higgs mechanism.

The dual gauge algebra matches the original when considering the quotient by broken generators.

Abstract

We consider M-theory compactified on a twisted 7-torus with fluxes when all the seven antisymmetric tensor fields in four dimensions have been dualized into scalars and thus the E_{7(7)} symmetry is recovered. We find that the Scherk--Schwarz and flux gaugings define a ``dual'' gauge algebra, subalgbra of E_{7(7)}, where some of the generators are associated with vector fields which are dual to part of the original vector fields (deriving from the 3-form). In particular they are dual to those vector fields which have been ``eaten'' by the antisymmetric tensors in the original theory by the (anti-)Higgs mechanism. The dual gauge algebra coincides with the original gauge structure when the quotient with respect to these dual (broken) gauge generators is taken. The particular example of the S-S twist corresponding to a ``flat group'' is considered.