Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

Abstract

We review the recent progress in studying the quantum structure of 6D, N = (1, 0) and N = (1, 1) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = (1, 0) 1 way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = (1, 1) supersymmetric Yang-Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Also some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Also in the abelian case we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

“…The main advantage of such a formulation is the possibility to keep manifest N = (1, 0) supersymmetry at all steps of quantum calculations. In our recent papers [44][45][46][47][48][49][50] we developed the harmonic superfield approach for calculating the lowest off-shell quantum corrections in various 6D, N = (1, 0) and N = (1, 1) supersymmetric theories. In the present paper we apply this superfield technique for studying the one-loop effective action in 6D, N = (1, 0) higher-derivative gauge theory of ref.…”

One-loop divergences in 6D, N $$ \mathcal{N} $$ = (1, 0) SYM theory

“…In our previous works [28][29][30][31][32][33] we studied UV properties of 6D, N = (1, 0) and N = (1, 1) theories in the 6D harmonic superspace formulation. In particular, it was found that 6D, N = (1, 1) theory is off-shell finite in the one-loop approximation in the Feynman gauge, although the divergences are still present in the non-minimal gauges [33] (they vanish on shell).…”