Cancellation of IR divergences in 3d Abelian gauge theories

Giovanni Galati (SISSA, Via Bonomea 265, Trieste, I-34136, Italy; INFN, Sezione di Trieste, Via Valerio 2, Trieste, I-34127, Italy) ; Marco Serone (SISSA, Via Bonomea 265, Trieste, I-34136, Italy; INFN, Sezione di Trieste, Via Valerio 2, Trieste, I-34127, 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.

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Published on:
16 February 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 2
Pages 1-20
DOI:
https://doi.org/10.1007/JHEP02(2022)123
arXiv:
2111.02124
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: