Four-Graviton Scattering and String Path Integral in the Proper-time gauge

TL;DR

This paper computes four-closed-string scattering amplitudes in the proper-time gauge, revealing differences from conventional results and highlighting the role of tachyon poles in quantum gravity and dark matter research.

Contribution

It provides a field theoretic expression for string scattering amplitudes using the proper-time gauge, uncovering discrepancies with traditional methods and emphasizing tachyon pole effects.

Findings

Zero-slope limit recovers Einstein gravity graviton scattering.

Finite slope amplitudes differ from conventional string theory results.

Presence of tachyon poles impacts short-distance gravitational interactions.

Abstract

We evaluate the four-closed-string scattering amplitude, using the Polyakov string path integral in the proper-time gauge. By identifying the Fock space representation of the four-closed-string-vertex, we obtain a field theoretic expression of the closed string scattering amplitudes. In the zero-slope limit, the four-closed-string scattering amplitude reduces to the four-graviton-scattering amplitude of Einstein's gravity. However, at a finite slope, the four-graviton scattering amplitude in the proper-time gauge differs not only from that of Einstein gravity, but also significantly differs from the conventional one obtained by using the vertex operator technique in string theory. This discrepancy is mainly due to the presence of closed string tachyon poles in the four-graviton-scattering amplitude, which are missing in previous works. Because the tachyon poles in the scattering amplitude considerably alter the short distance behavior of gravitational interaction, they may be important in understanding problems associated with the perturbative theory of quantum gravity and the dark matter within the framework of string theory.