Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry

TL;DR

This paper derives higher derivative corrections to eleven-dimensional supergravity using local supersymmetry, reducing a complex parameter space to two key invariants that align with string theory results.

Contribution

It introduces a systematic method to determine higher derivative supergravity corrections constrained by local supersymmetry, simplifying the parameter space to two main invariants.

Findings

Higher derivative corrections are characterized by two main parameters.

The bosonic parts match known string theory results.

Computer-aided checks confirm supersymmetry invariance.

Abstract

In this paper we derive higher derivative corrections to the eleven dimensional supergravity by applying the Noether method with respect to the N=1 local supersymmetry. An ansatz for the higher derivative effective action, which includes quartic terms of the Riemann tensor, is parametrized by 132 parameters. Then we show that by the requirement of the local supersymmetry, the higher derivative effective action is essentially described by two parameters. The bosonic parts of these two superinvariants completely match with the known results obtained by the perturbative calculations in the type IIA superstring theory. Since the calculations are long and systematic, we build the computer programming to check the cancellation of the variations under the local supersymmetry. This is an extended version of our previous paper hep-th/0508204.