Dual representation of lattice QCD with worldlines and worldsheets of abelian color fluxes

TL;DR

This paper introduces a novel dual representation of lattice QCD using worldlines and worldsheets derived from abelian color fluxes, enabling exact reformulation and closed-form coefficients for strong coupling expansions.

Contribution

It presents the first dual formulation of lattice QCD with explicit worldline and worldsheet variables using abelian color fluxes, applicable to pure gauge, strong coupling, and full QCD.

Findings

Dual variables form worldlines and worldsheets with exact constraints.

All expansion coefficients are known in closed form.

Applicable to pure SU(3), strong coupling, and full QCD cases.

Abstract

We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion and with the abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.