Settling an old story: solution of the Thirring model in thimble regularization

Abstract

Thimble regularisation of lattice field theories has been proposed as a solution to the infamous sign problem. It is conceptually very clean and powerful, but it is in practice limited by a potentially very serious issue: in general many thimbles can contribute to the computation of the functional integrals. Semiclassical arguments would suggest that the fundamental thimble could be sufficient to get the correct answer, but this hypothesis has been proven not to hold true in general. A first example of this failure has been put forward in the context of the Thirring model: the dominant thimble approximation is valid only in given regions of the parameter space of the theory. Since then a complete solution of this (simple) model in thimble regularisation has been missing. In this paper we show that a full solution (taking the continuum limit) is indeed possible. It is possible thanks to a method we recently proposed which de facto evades the need to simulate on many thimbles.