Z2 electric strings and center vortices in SU(2) lattice gauge theory

TL;DR

This paper investigates the role of Z2 electric strings and center vortices in SU(2) lattice gauge theory, revealing how electric strings contribute to the physical string tension despite their divergent density.

Contribution

It introduces a representation of SU(2) lattice gauge theory using center vortices and Z2 electric strings, highlighting the divergent behavior and their impact on Wilson loops.

Findings

Z2 electric string density diverges in the continuum limit

Electric strings contribute to the Wilson loop's string tension

Presence of Z2 topological monopoles affects statistical weights

Abstract

We study the representations of SU(2) lattice gauge theory in terms of sums over the worldsheets of center vortices and Z2 electric strings, i.e. surfaces which open on the Wilson loop. It is shown that in contrast to center vortices the density of electric Z2 strings diverges in the continuum limit of the theory independently of the gauge fixing, however, their contribution to the Wilson loop yields physical string tension due to non-positivity of their statistical weight in the path integral, which is in turn related to the presence of Z2 topological monopoles in the theory.