Sergei M. Kuzenko

On Low-Energy Effective Actions in N = 2, 4 Superconformal Theories in Four Dimensions

We study some aspects of low-energy effective actions in 4-d superconformal gauge theories on the Coulomb branch. We describe superconformal invariants constructed in terms of the N = 2 abelian vector multiplet which play the role of building blocks for the N = 2, 4 low-energy effective actions. We compute the one-loop effective actions in constant N = 2 field strength background in N = 4 SYM theory and in N = 2 SU(2) SYM theory with four hypermultiplets in the fundamental representation. Using a classification of superconformal invariants, we then find the manifestly N = 2 superconformal form of these effective actions. While our explicit computations are done in the one-loop approximation, our conclusions about the structure of the effective actions in N = 2 superconformal theories are general. We comment on some relations to supergravity–gauge theory duality in the description of D-brane interactions.

Projective superspace as a double punctured harmonic superspace

We analyze the relationship between the N=2 harmonic and projective superspaces, which are the only approaches developed to describe general N=2 super-Yang–Mills theories in terms of off-shell supermultiplets with conventional supersymmetry. The structure of low energy hypermultiplet effective action is briefly discussed.

Nonlinear Self-Duality and Supersymmetry ∗

We review self-duality of nonlinear electrodynamics and its extension to several Abelian gauge fields coupled to scalars. We then describe self-duality in supersymmetric models, both N = 1 and N = 2. The self-duality equations, which have to be satisfied by the action of any self-dual system, are found and solutions are discussed. One important example is the Born-Infeld action. We explain why the N = 2 supersymmetric actions proposed so far are not the correct world-volume actions for D3 branes in d = 6.

On the D=4, N=2 non-renormalization theorem

Abstract Using the harmonic superspace background field formulation for general D =4, N =2 super Yang-Mills theories, with matter hypermultiplets in arbitrary representations of the gauge group, we present the first rigorous proof of the N =2 non-renormalization theorem; specifically, the absence of ultraviolet divergences beyond the one-loop level. Another simple consequence of the background field formulation is the absence of the leading non-holomorphic correction to the low-energy effective action at two loops.

The CNM-hypermultiplet nexus

Abstract We consider additional properties of CNM (chiral-non-minimal) models. We show how 4D, N = 2 non-linear σ-models can be described solely in terms of N = 1 superfield CNM doublets. These actions are described by a Kahler potential together with an infinite number (in the general case) of terms involving its successively higher derivatives. We briefly discuss how N = 2 supersymmetric extension of the previously proposed N = 1 CNM low-energy QCD effective action can be achieved.

Comments on the Background Field Method in Harmonic Superspace: Non-holomorphic Corrections in N = 4 SYM

We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4SU(2) SYM effective action.

Effective action of the N = 2 Maxwell multiplet in harmonic superspace☆

Abstract We present, in the N = 2, D = 4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N = 2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N = 2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N = 2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U (1)-factor in the N = 2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic [Bcorrections arise at leading order. These holomorphic contribution are consistent with Seibergs quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N = 2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.

Non-holomorphic effective potential in N=4 SU(n) SYM

Abstract We compute the one-loop non-holomorphic effective potential for the N =4 SU ( n ) supersymmetric Yang-Mills theory with the gauge symmetry broken down to the maximal torus U (1) n −1 . Our approach remains powerful for arbitrary gauge groups and is based on the use of N =2 harmonic superspace formulation for general N =2 Yang-Mills theories along with the superfield background field method.

Superfield chiral effective potential

Abstract A superfield approach to compute the chiral effective superpotential in the Wess-Zumino model is developed. An explicit calculation of the potential in the two-loop approximation is described.

A GEOMETRIC MODEL OF THE ARBITRARY SPIN MASSIVE PARTICLE

A new model of the relativistic massive particle with arbitrary spin [the (m, s) particle] is suggested. The configuration space of the model is the product of Minkowski space and a two-dimensional sphere: ℳ6=ℝ3, 1×S2. The system describes Zitterbevegung at the classical level. Together with explicitly realized Poincare symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase space counterparts of the Casimir operators of the Poincare group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin s field.