Minimal gauge invariant couplings at order ${\ell }_p^6$ in M-theory

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.

arXiv comment41 pages, Latex file, no figure. arXiv admin note: substantial text overlap with arXiv:2006.09193; v2: the version appears in NPB

References in corpus (22)

• String Theory Dynamics In Various Dimensions
• One loop in eleven dimensions
• xTras: a field-theory inspired xAct package for Mathematica
• R^4 Couplings in M and Type II Theories
• On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
• D-instantons, Strings and M-theory
• Lectures on Superstring and M Theory Dualities
• Covariant One-Loop Amplitudes in D=11
• Heterotic Effective Action and Duality Symmetries Revisited
• Manifestly supersymmetric M-theory
• Supersymmetric Corrections to Eleven-Dimensional Supergravity
• On a supersymmetric completion of the R^4 term in IIB supergravity
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• Effective action of bosonic string theory at order ${\alpha }^{\prime 2}$
• Toward the Determination of R^3F^2 Terms in M-theory
• On a supersymmetric completion of the $R^4$ term in type IIB supergravity
• On the supersymmetric completion of the $R^4$ term in M-theory
• Minimal independent couplings at order ${\alpha }^{\prime 2}$
• Higher-derivative gauge field terms in the M-theory action
• On NS-NS couplings at order ${\alpha }^{\prime 3}$
• Minimal gauge invariant couplings at order ${\alpha }^{\prime 3}$: NS-NS fields
• Gauge field corrections to 11-dimensional supergravity via dimensional reduction