Low-energy effective actions in N=2, 4 superconformal theories in four dimensions

Abstract

We study some aspects of low-energy effective actions in $4d$ 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 a 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.