Effective actions in N = 1 $$ \mathcal{N}=1 $$ , D5 supersymmetric gauge theories: harmonic superspace approach

Abstract

Abstract:We consider the off-shell formulation of the 5D, N = 1 super Yang-Mills and super Chern-Simons theories in harmonic superspace. Using such a formulation we develop a manifestly supersymmetric and gauge invariant approach to constructing the one-loop effective action both in super Yang-Mills and super Chern-Simons models. On the base of this approach we compute the leading low-energy quantum contribution to the effective action on the Abelian vector multiplet background. This contribution corresponds to the 'F 4 ' invariant which is given in 5D superfield form.

Superfield realization of hidden R-symmetry in extended supersymmetric gauge theories and its applications

“…The part of the superfield N = 1 SYM effective action containing the component four-derivative term of gauge field reads [11]…”

Quantum calculation of the low-energy effective action in 5D, N=2 SYM theory

“…Throughout the paper we use the notations and conventions of [11] and [14]. We formulate N = 2 SYM theory in 5D, N = 1 harmonic superspace in terms of the gauge superfield V ++ and the hypermultiplet one q + a ≡ (q + , −q + ), a = 1, 2, both being analytic.…”

“…We construct the one-loop effective action for N = 2 SYM theory with the "microscopic" action (2.1) within the background superfield field formulation. The background superfield method in 5D, N = 1 harmonic superspace [14] is a direct generalization of the 4D, N = 2 one [18][19][20][21] and it is based on the background-quantum splitting of the initial superfields into the 'background' V ++ , Q + a and the 'quantum' v + , q + a parts:…”

“…The theory is manifestly N = 1 supersymmetric and, in addition, possesses an implicit on-shell N = 1 supersymmetry. Its effective action in the N = 1 gauge multiplet sector was calculated some time ago in [14]. Like in the 4D, N = 4 case, the total N = 2 supersymmetric effective action of this theory was restored in [11] through the completion of the N = 1 gauge multiplet action by the proper hypermultiplet-dependent terms, such that the full expression for the effective action respect the additional implicit N = 1 supersymmetry.…”

“…To preserve the classical symmetries in the quantum case, we make use of the background superfield method in 5D, N = 1 harmonic superspace. It is a 5D version of the method developed earlier in [14,15] (see also [16]). Following the approach of [11], we formulate 5D, N = 2 gauge multiplet as a collection of N = 1 gauge multiplet and the hypermultiplet, both being in the adjoint representation of gauge group.…”