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.
Highlights
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
In particular we show that specific gauge-variant correlators, including the two-point function of matter fields, are IR finite to all orders in perturbation theory
Summary
Consider a 3d Euclidean abelian gauge theory coupled to matter. The latter can be made of scalars or fermions, or both. We would like to show that arbitrary correlation functions of gauge-invariant operators based on the action (2.1) are IR finite. To all orders in perturbation theory, for small momentum p the effective photon propagator goes like the tree-level one, ∝ 1/p2.6 Any internal photon line has to attach to a pair of γ(n)’s or to the same γ(n). In both cases the vertices bring two powers of p, precisely canceling the 1/p2 factor for each photon line. Building on the above argument, we can prove the IR finiteness of arbitrary correlation functions of gauge-invariant operators Oi made of matter and/or photon elementary constituents. It should be emphasized that individual Feynman diagrams can be IR divergent and it is only when summed together that such IR divergences are guaranteed to cancel
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
