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On dynamical mass generation in three dimensional supersymmetric U(1) gauge field theory

A. Campbell-Smith·N. E. Mavromatos
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Abstract

We investigate and contrast the non-perturbative infra red structure of N=1 and N=2 supersymmetric non-compact U(1) gauge field theory in three space-time dimensions with N matter flavours. We study the Dyson-Schwinger equations in a general gauge using superfield formalism; this ensures that supersymmetry is kept manifest, though leads to spurious infra red divergences which we have to avoid carefully. In the N=1 case the superfield formalism allows us to choose a vertex which satisfies the U(1) Ward identity exactly, and we find the expected critical behaviour in the wavefunction renormalization and strong evidence for the existence of a gauge independent dynamically generated mass, but with no evidence for a critical flavour number. We study the N=2 model by dimensional reduction from four dimensional N=1 electrodynamics, and we refine the old gauge dependence argument that there is no dynamical mass generation. We recognize that the refinement only holds after dimensional reduction.

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A. Campbell-Smith, N. E. Mavromatos. 1999-04-26. On dynamical mass generation in three dimensional supersymmetric U(1) gauge field theory. https://doi.org/10.1103/physrevd.60.105011

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