String gravity in D=4

Pablo A Cano,Alejandro Ruipérez

doi:10.1103/physrevd.105.044022

Abstract

We revisit the four-dimensional theory of gravity that arises from string theory with higher-derivative corrections. By compactifying and truncating the ten-dimensional effective action of heterotic string theory at first order in $\alpha'$, and carefully dealing with field redefinitions, we show that the four-dimensional theory takes the form of an axidilaton model where the scalars couple to the Gauss-Bonnet and Pontryagin densities. Thus, the actual string gravity is a generalization of the well-studied Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons models. Using this action we compute the stringy corrections to the Kerr geometry and we obtain, for the first time, the corrections to the entropy of the Kerr black hole at order $\alpha'^2$. We check that the first law of black hole mechanics is satisfied and discuss several properties of the solution. Our results suggest that there exist black hole solutions with $J>M^2$ and therefore the extremal ratio $J/M^2$ must be modified positively.

Highlights

String theory is thought to provide a quantum theory of gravity and a unified framework for all the forces of nature
By compactifying and truncating the ten-dimensional effective action of heterotic string theory at first order in α0, and carefully dealing with field redefinitions, we show that the four-dimensional theory takes the form of an axidilaton model where the scalars couple to the Gauss-Bonnet and Pontryagin densities
For the terms in (30) that are quadratic in the zeroth order equations of motion (EOM), these Oðα02Þ corrections generated by the redefinitions are still proportional to the EOM and they can be further removed by an additional redefinition

Summary

INTRODUCTION

String theory is thought to provide a quantum theory of gravity and a unified framework for all the forces of nature It possesses a huge landscape of low-energy effective theories that include all sorts of interactions, many for which we do not have any experimental evidence. The low-energy limit of the different types of string theories can be described by ten-dimensional supergravity actions with higher-derivative corrections [1–7]. The compactification of these actions down to four dimensions leads to effective theories with many scalar and vector fields coupled to gravity, but it is interesting to ask what is the minimal truncation one could perform of these theories. It is a quite extended lore that, in four dimensions, the effective action of heterotic string theory is captured by the so-called Einstein-dilaton-Gauss-Bonnet (EdGB) theory [11–14],

Z pffiffiffiffiffi 1

HETEROTIC SUPERSTRING EFFECTIVE ACTION IN FOUR DIMENSIONS

THE KERR BLACK HOLE AT ORDER α02

CONCLUSIONS