Cancellation of IR divergences in 3d Abelian gauge theories
Giovanni Galati (INFN, Sezione di Trieste, Via Valerio 2, Trieste, I-34127, Italy, SISSA, Via Bonomea 265, Trieste, I-34136, Italy); Marco Serone (INFN, Sezione di Trieste, Via Valerio 2, Trieste, I-34127, Italy, SISSA, Via Bonomea 265, Trieste, I-34136, Italy)
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.