https://doi.org/10.1140/epjc/s10052-019-7291-5
Regular Article - Theoretical Physics
On missing Bianchi identities in cohomology formulation
1
Dipartimento di Fisica, Universita di Roma “Tor Vergata”, and I.N.F.N. Sezione di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133, Rome, Italy
2
Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain
3
Abdus Salam ICTP, Strada Costiera 11, 34151, Trieste, Italy
4
Yau Mathematical Sciences Center, Tsinghua University, Haidian District Beijing, 100084, China
* e-mail: pshukla@ictp.it
Received:
30
April
2019
Accepted:
9
September
2019
Published online:
21
September
2019
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. These identities have been mostly overlooked in the previous attempts of studying moduli stabilization, particularly for the models developed in the beyond toroidal frameworks, where they could play some important role.
© The Author(s), 2019
