Minimal gauge invariant couplings at order $\ell_p^6$ in M-theory

TL;DR

This paper systematically classifies gauge invariant couplings at order  in M-theory, identifying minimal independent couplings and relating some to type IIA superstring theory results.

Contribution

It provides a comprehensive enumeration of independent gauge invariant couplings at order  in M-theory, including their schemes and derivative structures, and connects them to string theory.

Findings

Minimum of 1062 independent couplings identified.

Existence of schemes with no couplings involving certain curvature and derivative terms.

Coupling with more than two derivatives is found to be zero.

Abstract

Removing the field redefinitions, the Bianchi identities and the total derivative freedoms from the general form of the gauge invariant couplings at order $\ell_p^6$ for the bosonic fields of M-theory, we have found that the minimum number of independent couplings in the structures with even number of the three-form, is 1062. We find that there are schemes in which there is no coupling involving $R,\,R_{\mu\nu},\,\nabla_\mu F^{\mu\alpha\beta\gamma}$. In these schemes, there are sub-schemes in which, except one coupling which has the second derivative of $F^{(4)}$, the couplings can have no term with more than two derivatives. We find some of the parameters by dimensionally reducing the couplings on a circle and comparing them with the known couplings of the one-loop effective action of type IIA superstring theory. In particular, we find the coupling which has term with more than two derivatives is zero.