Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge

Taejin Lee

doi:10.1051/epjconf/201816807004

Abstract

We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.

Highlights

Construction of a finite quantum theory of gravity was the main motivation for theorists to turn towards the string theory [1] as it has become clear that the perturbative theory of gravity based on the quantum field theory [2,3,4] is not renormalizable [5, 6]
In the process of evaluating the string scattering, we find that the Fock space representations of the closed string field theory are completely factorized into those of the open string field theory in general: This factorization indicates that the KLT [13] relations of the first quantized string theory may be fully extended to the second quantized string theory
Having obtained the Fock space representation of the three-closed-string vertex, we shall calculate the three-graviton-scattering amplitude to confirm that the closed string field theory, as a consistent quantum theory of gravity reduces to the Einstein gravity in the low energy domain

Summary

Introduction

Construction of a finite quantum theory of gravity was the main motivation for theorists to turn towards the string theory [1] as it has become clear that the perturbative theory of gravity based on the quantum field theory [2,3,4] is not renormalizable [5, 6]. We construct the covariant closed string field theory by extending recent works on open string field theory in the proper-time gauge [7,8,9,10,11]. In the process of evaluating the string scattering, we find that the Fock space representations of the closed string field theory are completely factorized into those of the open string field theory in general: This factorization indicates that the KLT [13] relations of the first quantized string theory may be fully extended to the second quantized string theory

Closed string field theory in the proper-time gauge

Fock space representation of the closed string field theory

Three-graviton scattering amplitude

Conclusions