Derive Lovelock gravity from string theory in cosmological background

Peng Wang,Shuxuan Ying,Houwen Wu,Haitang Yang

doi:10.1007/jhep05(2021)218

Peng Wang, Shuxuan Ying + Show 2 more

Open Access

https://doi.org/10.1007/jhep05(2021)218

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Abstract

It was proved more than three decades ago, that the first order α′ 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 α′ 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.

Highlights

Peng Wang,a Houwen Wu,a Haitang Yanga and Shuxuan Yingb aCollege of Physics, Sichuan University, 29 Wangjiang Road, Chengdu, 610065, China bDepartment of Physics, Chongqing University, 55 South University Town Road, Chongqing, 401331, China E-mail: pengw@scu.edu.cn, iverwu@scu.edu.cn, hyanga@scu.edu.cn, ysxuan@cqu.edu.cn. It was proved more than three decades ago, that the first order α correction of string effective theory could be written as the Gauss-Bonnet term, which is the quadratic term of Lovelock gravity
An extension of general relativity requires the generalized Einstein tensor to respect three conditions: 1) It is symmetric; 2) It is divergence free (Bianchi identity); 3) Higher derivatives of the metric are absent in the EOM
Since string theory itself is ghost free, it is believed that the higher derivative pathology is caused by artificial truncation and can be cured by arranging the terms properly

Summary

Introduction

An extension of general relativity requires the generalized Einstein tensor to respect three conditions: 1) It is symmetric; 2) It is divergence free (Bianchi identity); 3) Higher derivatives of the metric are absent in the EOM (ghost free). Derive Lovelock gravity from string theory in cosmological background With an appropriate field redefinition, we reorganize the infinite α corrections of string effective action into a finite term expression for any specific dimension. This finite term expression matches Lovelock gravity exactly and fix the couplings of Lovelock gravity by the coefficients of string effective action.

Results

Conclusion