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

TL;DR

This paper develops a covariant closed string field theory in the proper-time gauge, demonstrating its relation to open string theory and deriving graviton scattering amplitudes, thus extending the KLT relations to second quantization.

Contribution

It constructs a covariant closed string field theory in the proper-time gauge and shows its Fock space factorization into open string theory, promoting KLT relations to second quantization.

Findings

Closed string field theory can be constructed covariantly in the proper-time gauge.

Fock space representations of closed strings factorize into open string representations.

Explicit calculation of three-graviton scattering amplitudes confirms the theory's validity.

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.