The robustness of the vacuum wave function and other matters for Yang-Mills theory

TL;DR

This paper investigates the stability and fundamental structure of the vacuum wave function in (2+1)-dimensional Yang-Mills theory, emphasizing its robustness against regularization choices and exploring related gauge-invariant configurations.

Contribution

It demonstrates that the vacuum wave function's leading Gaussian term is determined by gauge anomaly and Lorentz symmetry, highlighting its robustness and insensitivity to regularization methods.

Findings

The vacuum wave function's Gaussian form is robust and determined by fundamental symmetries.

The wave function shows insensitivity to regularization choices.

Comments on gauge-invariant configuration space in Euclidean three-dimensional gauge fields.

Abstract

In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the (2+1)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of (2+1)-dimensional Yang-Mills theory. This is to highlight the robustness of the wave function and its relative insensitivity to the choice of regularizations. We then comment on the correspondence with the explicit calculations done in earlier papers. We also make some comments on the nature of the gauge-invariant configuration space for Euclidean three-dimensional gauge fields (relevant to (3+1)-dimensional Yang-Mills theory).