Quantum N=3, d=3 Chern-Simons Matter Theories in Harmonic Superspace

TL;DR

This paper develops a superspace method for N=3, d=3 Chern-Simons matter theories, proving their finiteness and analyzing quantum corrections, including the emergence of super Yang-Mills action.

Contribution

It introduces a background field approach in harmonic superspace, establishes a nonrenormalization theorem, and computes key supergraph propagators and corrections.

Findings

Proves ultra-violet finiteness of N=3, d=3 Chern-Simons matter theories.

Derives explicit superfield propagators in a Chern-Simons background.

Shows quantum corrections induce super Yang-Mills action instead of Chern-Simons.

Abstract

We develop the background field method for studying classical and quantum aspects of N=3, d=3 Chern-Simons and matter theories in N=3 harmonic superspace. As one of the immediate consequences, we prove a nonrenormalization theorem implying the ultra-violet finiteness of the corresponding supergraph perturbation theory. We also derive the general hypermultiplet and gauge superfield propagators in a Chern-Simons background. The leading supergraphs with two and four external lines are evaluated. In contrast to the non-supersymmetric theory, the leading quantum correction to the massive charged hypermultiplet proves to be the super Yang-Mills action rather than the Chern-Simons one. The hypermultiplet mass is induced by a constant triplet of central charges in the N=3, d=3 Poincare superalgebra.