Thimble regularization at work besides toy models: from Random Matrix Theory to Gauge Theories

TL;DR

This paper explores the effectiveness of thimble regularization in addressing the sign problem in realistic models, including a detailed study of Chiral Random Matrix theory and prospects for gauge theories.

Contribution

It extends thimble regularization from toy models to complex, realistic models like Chiral Random Matrix theory, analyzing thimble contributions and algorithm robustness.

Findings

Multiple thimbles contribute to the solution.

Algorithms can be designed to stay on the correct manifold.

Chiral Random Matrix theory exhibits a significant sign problem.

Abstract

Thimble regularization as a solution to the sign problem has been successfully put at work for a few toy models. Given the non trivial nature of the method (also from the algorithmic point of view) it is compelling to provide evidence that it works for realistic models. A Chiral Random Matrix theory has been studied in detail. The known analytical solution shows that the model is non-trivial as for the sign problem (in particular, phase quenched results can be very far away from the exact solution). This study gave us the chance to address a couple of key issues: how many thimbles contribute to the solution of a realistic problem? Can one devise algorithms which are robust as for staying on the correct manifold? The obvious step forward consists of applications to gauge theories.