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.
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Galati, G., Serone, M. Cancellation of IR divergences in 3d Abelian gauge theories. J. High Energ. Phys. 2022, 123 (2022). https://doi.org/10.1007/JHEP02(2022)123
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DOI: https://doi.org/10.1007/JHEP02(2022)123