Gauge-invariant critical exponents for the Ginzburg-Landau model

TL;DR

This paper presents a gauge-invariant approach to calculating critical exponents in the Ginzburg-Landau model, confirming consistency with traditional covariant gauge results through perturbative expansions.

Contribution

It introduces a gauge-invariant formulation for critical exponents and computes them to first order in specific expansions, aligning with known covariant gauge outcomes.

Findings

Gauge-invariant correlation-function exponent matches covariant gauge results.

First-order calculations in 4-d and 1/n expansions are consistent with previous methods.

Provides a new framework for analyzing critical behavior in gauge theories.

Abstract

The critical behavior of the Ginzburg-Landau model is described in a manifestly gauge-invariant manner. The gauge-invariant correlation-function exponent is computed to first order in the $4-d$ and $1/n$-expansion, and found to agree with the ordinary exponent obtained in the covariant gauge, with the parameter $\alpha=1-d$ in the gauge-fixing term $(\partial_\mu A_\mu)^2 /2 \alpha$.