Cancellation of IR divergences in 3d Abelian gauge theories

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.

Automated summary

This article investigates the issue of infrared divergences in three dimensional abelian gauge theories in a Coulomb phase. By utilizing generalizations of Ward-Takahashi identities, it is shown that correlation functions of gauge-invariant operators are infrared finite in all orders of perturbation theory. It is also demonstrated that certain gauge-variant correlators, including the two-point function of matter fields, are also infrared finite in perturbation theory. Possible applications of these findings are briefly discussed.