On the construction of Chern-Simons terms in the presence of flux

TL;DR

This paper presents a method to derive boundary effective actions and fluxed Chern-Simons terms in lower dimensions from higher-dimensional theories, with applications to supergravity and flux compactifications.

Contribution

It introduces a novel approach to relate boundary actions to fluxed Chern-Simons terms across dimensions, specifically deriving 11D supergravity terms from 12D theories.

Findings

Derived 11D supergravity Chern-Simons terms with flux from 12D theories.

Established a systematic method for relating boundary actions to fluxed Chern-Simons terms.

Applied the construction to orbifolds and flux backgrounds in supergravity.

Abstract

We develop a method for relating the boundary effective action associated with an orbifold of the D+1 dimensional theory of a p-form field to D dimensional fluxed Chern-Simons type of terms. We apply the construction to derive from twelve dimensions the Chern-Simons terms of the eleven dimensional supergravity theory in the presence of flux.