Cancellation of IR Divergences in 3d Abelian Gauge Theories

TL;DR

This paper demonstrates that in 3d abelian gauge theories, all gauge-invariant correlation functions are IR finite at all orders, with some gauge-variant correlators also showing finiteness, challenging previous expectations about IR divergences.

Contribution

The authors prove IR finiteness of gauge-invariant correlators in 3d abelian gauge theories using generalized Ward-Takahashi identities, extending understanding of IR behavior.

Findings

Gauge-invariant correlators are IR finite to all orders.

Certain gauge-variant correlators, including matter two-point functions, are also IR finite.

Gauge invariance is sufficient but not necessary for IR finiteness.

Abstract

Three dimensional abelian gauge theories classically in a Coulomb phase are affected by IR divergences even when the matter fields are all massive. Using generalizations of Ward-Takahashi identities, we show that correlation functions of gauge-invariant operators are IR finite to all orders in perturbation theory. Gauge invariance is sufficient but not necessary for IR finiteness. In particular we show that specific gauge-variant correlators, including the two-point function of matter fields, are also IR finite to all orders in perturbation theory. Possible applications of these results are briefly discussed.