On Missing Bianchi Identities in Cohomology Formulation

Understand

In this article, we perform a deep analysis of the Bianchi identities in the two known formulations developed for the four-dimensional effective type IIA supergravity theory with (non-)geometric fluxes.

• In what we call the `first formulation', fluxes are expressed in the real six-dimensional indices while in the `second formulation', fluxes are written in the cohomology form.
• We find that the set of flux constraints arising from these two known formulations are not equivalent, and there are missing identities in the cohomology version which need to be supplemented to match with the first formulation.
• By analyzing two explicit examples, we conjecture a model independent form for (the most of) the missing identities.