Derive Lovelock Gravity from String Theory in Cosmological Background

TL;DR

This paper demonstrates that the first order $mbda'$ corrections of string effective theory in a cosmological background can be exactly reformulated as Lovelock gravity, linking string theory corrections to a well-known gravitational theory.

Contribution

It shows how string theory's infinite $mbda'$ corrections can be reorganized into a finite Lovelock gravity form, fixing the couplings from string coefficients.

Findings

Exact match between string corrections and Lovelock gravity in cosmological background

Finite expression for $mbda'$ corrections in any specific dimension

Provides strong support for string theory's validity

Abstract

It was proved more than three decades ago, that the first order $\alpha'$ correction of string effective theory could be written as the Gauss-Bonnet term, which is the quadratic term of Lovelock gravity. In cosmological background, with an appropriate field redefinition, we reorganize the infinite $\alpha'$ corrections of string effective action into a finite term expression for any specific dimension. This finite term expression matches Lovelock gravity exactly and thus fix the couplings of Lovelock gravity by the coefficients of string effective action. This result thus provides a strong support to string theory.