The background field method for N=2 super Yang-Mills theories in harmonic superspace

Abstract

The background field method for N = 2 super Yang-Mills theories in harmonic superspace is developed. The ghost structure of the theory is investigated. It is shown that the ghosts include two fermionic real ω-hypermultiplets (FaddeevPopov ghosts) and one bosonic real ω-hypermultiplet (Nielsen-Kallosh ghost), all in the adjoint representation of the gauge group. The one-loop effective action is analysed in detail and it is found that its structure is determined only by the ghost corrections in the pure super Yang-Mills theory. As applied to the case of N = 4 super Yang-Mills theory, realized in terms of N = 2 superfields, the latter result leads to the remarkable conclusion that the one-loop effective action of the theory does not contain quantum corrections depending on the N = 2 gauge superfield only. We show that the leading low-energy contribution to the one-loop effective action in the N = 2 SU (2) super Yang-Mills theory coincides with Seiberg's perturbative holomorphic effective action.

Exact effective couplings of four dimensional gauge theories withN=2supersymmetry

“…For simplicity, we present only the Yang Mills part of the theory, but the procedure carries over to quarks and also to supersymmetric N = 1 and N = 2 theories in the appropriate superspace [27][28][29][30].…”

Complete low-energy effective action in SYM: a direct supergraph calculation

“…As the result we are aware of the unified approach allowing us to compute the low-energy effective action in both the gauge multiplet and hypermultiplet sectors. The calculations are carried out within the N = 2 background field method [17], with making use of the quantum N = 2 harmonic superfield techniques pioneered in [14] and further advanced in [12], [16]- [21].…”

Improved methods for hypergraphs

“…In fact, background field formalism in harmonic superspace has quite a straightforward construction [7]. Although the construction has some subtleties, it has been refined in a series of papers along with relevant calculations [8,9,10,11].…”