Wilson loops with arbitrary charges

TL;DR

The paper introduces a method to define and compute Wilson loops with arbitrary real powers in lattice gauge theories, revealing limitations with non-integer fluxes and proposing a new continuum limit where such observables are meaningful.

Contribution

It demonstrates how to implement arbitrary powers of Wilson loops in lattice gauge theories and identifies a new continuum limit where these observables are well-defined.

Findings

Arbitrary real powers of Wilson loops can be defined in lattice gauge theories.

Non-integer fluxes cannot be excited in the spectrum of the theory.

A new continuum limit allows for meaningful observables with arbitrary charges.

Abstract

We discuss how to implement, in lattice gauge theories, external charges which are not commensurate with an elementary gauge coupling. It is shown that an arbitrary, real power of a standard Wilson loop (or Polyakov line) can be defined and consistently computed in lattice formulation of non-abelian, two dimensional gauge theories. However, such an observable can excite quantum states with integer fluxes only. Since the non-integer fluxes are not in the spectrum of the theory they cannot be created, no matter which observable is chosen. Also the continuum limit of above averages does not exist unless the powers in question are in fact integer. On the other hand, a new continuum limit exists, which is rather intuitive, and where above observables make perfect sense and lead to the string tension proportional to the square of arbitrary (non necessary commensurate with gauge coupling) charge.