Dual Computations of Non-abelian Yang-Mills on the Lattice

TL;DR

This paper develops and tests an algorithm for numerical computations in non-abelian SU(2) Yang-Mills theories on the lattice using dual models, demonstrating its effectiveness through spin expectation value calculations.

Contribution

It introduces a new efficient algorithm for non-abelian dual computations on the lattice, building on recent spin foam methods and addressing previous open problems.

Findings

Algorithm successfully computes spin expectation values

Results agree with conventional lattice computations

Demonstrates practicality of dual methods for non-abelian gauge theories

Abstract

In the past several decades there have been a number of proposals for computing with dual forms of non-abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet non-trivial case in which the gauge group is non-abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest.