Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate

TL;DR

This paper introduces a stochastic method to compute high-order perturbative coefficients in lattice gauge theory, successfully extending the series for the SU(3) plaquette up to four loops, enhancing precision in lattice calculations.

Contribution

A novel stochastic technique for calculating perturbative expansion coefficients in lattice gauge theory, enabling extension to higher loop orders.

Findings

Extended the perturbative series for the SU(3) plaquette to four loops.

Demonstrated the effectiveness of the stochastic method in lattice calculations.

Provided numerical results for the weak coupling expansion coefficients.

Abstract

We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables $U_\mu(x) \to \exp\{A_\mu(x)/\sqrt\beta\}$ into the Langevin algorithm and the observables and to perform the expansion in \beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by one loop the previously known series.