Anomalous Dimension of Dirac's Gauge-Invariant Nonlocal Order Parameter in Ginzburg-Landau Field Theory

TL;DR

This paper calculates the anomalous dimension of a gauge-invariant nonlocal order parameter in Ginzburg-Landau theory, providing exact results for various dimensions and field numbers, and confirming gauge invariance.

Contribution

It presents an exact calculation of the anomalous dimension of Dirac's gauge-invariant order parameter across different dimensions and field counts, extending previous gauge-dependent results.

Findings

Exact anomalous dimension for all n at first order in epsilon.

Results valid for all dimensions between 2 and 4 at first order in 1/n.

Agreement with previous gauge-dependent exponents in Landau gauge.

Abstract

In a Ginzburg-Landau theory with $n$ fields, the anomalous dimension of the gauge-invariant nonlocal order parameter defined by the long-distance limit of Dirac's gauge-invariant two-point function is calculated. The result is exact for all $n$ to first order in $\epsilon \equiv 4-d$, and for all $d\in (2,4)$ to first order in $1/n$, and coincides with the previously calculated gauge-dependent exponent in the Landau gauge.