An example of optimal field cut in lattice gauge perturbation theory

TL;DR

This paper introduces an optimal field cut method in lattice gauge theory that transforms the divergent perturbative series into a convergent one, enabling accurate interpolation between weak and strong coupling regimes.

Contribution

It proposes a novel field cut technique that regularizes the perturbative series in lattice gauge theory, improving convergence and accuracy over traditional methods.

Findings

The modified series converges with a finite radius of convergence.

Optimal field cuts can be estimated using strong coupling expansion.

The method accurately interpolates between weak and strong coupling regimes.

Abstract

We discuss the weak coupling expansion of a one plaquette SU(2) lattice gauge theory. We show that the conventional perturbative series for the partition function has a zero radius of convergence and is asymptotic. The average plaquette is discontinuous at g^2=0. However, the fact that SU(2) is compact provides a perturbative sum that converges toward the correct answer for positive g^2. This alternate methods amounts to introducing a specific coupling dependent field cut, that turns the coefficients into g-dependent quantities. Generalizing to an arbitrary field cut, we obtain a regular power series with a finite radius of convergence. At any order in the modified perturbative procedure, and for a given coupling, it is possible to find at least one (and sometimes two) values of the field cut that provide the exact answer. This optimal field cut can be determined approximately using the strong coupling expansion. This allows us to interpolate accurately between the weak and strong coupling regions. We discuss the extension of the method to lattice gauge theory on a D-dimensional cubic lattice.