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

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.Comment: 1+37 pages, 3 figures; v2: a reference added, to appear in JHE

Higher-Derivative Terms in N=2 Supersymmetric Effective Actions

We show how to systematically construct higher-derivative terms in effective actions in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. Making an assumption about the absence of certain superspace Chern-Simons-like terms involving vector multiplets, we write all 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. These holomorphic terms include a novel 3-derivative term on mixed branches given as an integral over 3/4 of superspace. As an illustration of our method, we search for Wess-Zumino terms in the low energy effective action of N=2 supersymmetric QCD. We show that such terms occur only on mixed branches. We also present an argument showing that the combination of space-time locality with supersymmetry implies locality in the anticommuting superspace coordinates of for unconstrained superfields.Comment: 30 pages. Added references and simplified final form of WZ ter

Construction of one-loop N=4{\cal N}=4 SYM effective action on the mixed branch in the harmonic superspace approach

We develop a systematic approach to construct the one-loop ${\cal N}=4$ SYM effective action depending on both ${\cal N}=2$ vector multiplet and hypermultiplet background fields. Beginning with the formulation of ${\cal N}=4$ SYM theory in terms of ${\cal N}=2$ harmonic superfields, we construct the one-loop effective action using the covariant ${\cal N}=2$ harmonic supergraphs and calculate it in ${\cal N}=2$ harmonic superfield form for constant Abelian strength $F_{mn}$ and corresponding constant hypermultiplet fields. The hypermultiplet-dependent effective action is derived and given by integral over the analytic subspace of harmonic superspace. We show that each term in the Schwinger-De Witt expansion of the low-energy effective action is written as integral over full ${\cal N}=2$ superspace.Comment: 35 pages, JHEP styl

ABJM models in N=3 harmonic superspace

We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the N=3, d=3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The N=3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar potential of ABJM emerges after the elimination of auxiliary fields. Besides the original U(N)xU(N) ABJM model, we also construct N=3 superfield formulations of some generalizations. For the SU(2)xSU(2) case we give a simple superfield proof of its enhanced N=8 supersymmetry and SO(8) R-symmetry.Comment: 1+35 pages, minor changes, a reference added, published versio

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 N=2 abelian vector multiplet which play the role of building blocks for the N=2,4 supersymmetric 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 fundamental representation. Using the 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 applications to supergravity - gauge theory duality in the description of D-brane interactions.Comment: 18 pages, latex, comments/reference adde