Cancellation of IR Divergences in 3d Abelian Gauge Theories

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.

arXiv comment22 pages; V2: JHEP published version

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