Minimal unitary representations from supersymmetry

TL;DR

This paper derives supersymmetry constraints on R^4 and higher derivative corrections in maximal supergravity across various dimensions, revealing differential equations that govern scalar functions and implications for string theory effective actions.

Contribution

It provides explicit tensorial differential equations for scalar functions multiplying R^4 terms in supergravity, extending to higher derivatives and analyzing their solutions and string theory implications.

Findings

Second order derivatives vanish in dimensions below six.

Differential equations for scalar functions are derived from supersymmetry constraints.

Implications for non-perturbative string theory effective actions are discussed.

Abstract

We compute the supersymmetry constraints on the R^4 type corrections in maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial differential equations satisfied by the function of the scalar fields multiplying the R^4 term in the corresponding invariants. The second order derivative of this function restricted to the Joseph ideal vanishes in dimension lower than six. These results are extended to the d^4 R^4 and the d^6 R^4 corrections, based on the harmonic superspace construction of these invariants in the linearised approximation. We discuss the solutions of these differential equations and analysis the consequences on the non-perturbative type II low energy string theory effective action.