Minimizing gauge-functional for 2-d gravity and string theory

TL;DR

This paper introduces a minimizing procedure to select unique representatives of Riemann surfaces in string theory, simplifying the string path integral and addressing the Gribov ambiguity.

Contribution

It proposes a novel minimizing functional that reduces the string path integral to a specific fundamental domain, clarifying gauge fixing issues.

Findings

Existence of a minimizing procedure for Riemann surface representatives

Reduction of string path integral to a unique fundamental domain

Clarification of the Gribov problem in string theory

Abstract

We show the existence of a minimizing procedure for selecting a unique representative on the orbit of any given Riemann surface that contributes to the string partition function. As it must, the procedure reduces the string path integral to a final integration over a particular fundamental domain, selected by the choice of the minimizing functional. This construction somehow demystifies the Gribov question.