A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory

TL;DR

This paper introduces a novel method to address the complex-action problem in Monte Carlo simulations, successfully applied to a superstring theory model, revealing insights into the emergence of 4-dimensional space-time.

Contribution

The authors propose a general factorization-based approach that completely overcomes the overlap problem in complex-action Monte Carlo simulations, demonstrated through a nonperturbative superstring study.

Findings

Distribution function is positive definite in the superstring model

Method provides an intuitive explanation for 4d space-time emergence

Successfully reduces the complex-action problem in nonperturbative simulations

Abstract

Monte Carlo simulations of a system whose action has an imaginary part are considered to be extremely difficult. We propose a new approach to this `complex-action problem', which utilizes a factorization property of distribution functions. The basic idea is quite general, and it removes the so-called overlap problem completely. Here we apply the method to a nonperturbative study of superstring theory using its matrix formulation. In this particular example, the distribution function turns out to be positive definite, which allows us to reduce the problem even further. Our numerical results suggest an intuitive explanation for the dynamical generation of 4d space-time.