The fate of flat directions in higher derivative gravity

TL;DR

This paper investigates how flat directions in higher derivative gravity theories behave, showing that some remain unchanged while others are fixed when higher derivative corrections are included, with implications for black hole and string theory solutions.

Contribution

It provides explicit analysis of flat directions in higher derivative supergravity and string theory, revealing which directions are lifted or remain flat after corrections.

Findings

Flat directions in five-dimensional supergravity are not lifted by higher derivative terms.

In type IIB string theory, certain flat directions are fixed by higher derivative corrections.

Results hold for both supersymmetric and non-supersymmetric deformations.

Abstract

We discuss the fate of flat directions in higher derivative gravity by studying two explicit examples, namely higher derivative gauged supergravity in five dimensions and higher derivative type IIB string theory in ten dimensions. In the first case, the supersymmetric spinning black hole solution in asymptotically AdS spacetime, found by Gutowski and Reall, is analyzed. In this case we find that the flat direction at the two derivative level is not lifted after addition of higher derivative terms, and as it turns out, this result holds even for non-supersymmetric deformations of the higher derivative action. For the rotating D3-brane solutions in type IIB theory, the dilaton parametrizes a flat direction at leading order, but its fate changes upon including order (\alpha^\prime)^3 supersymmetric higher derivative corrections to the type IIB action, i.e. its leading value gets fixed.