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

TL;DR

This paper investigates the structure of low-energy effective actions in four-dimensional N=2 and N=4 superconformal gauge theories, focusing on superconformal invariants and one-loop computations, with implications for supergravity and D-brane interactions.

Contribution

It introduces superconformal invariants for N=2 theories and derives their effective actions in one-loop approximation, providing a general framework for understanding these theories.

Findings

Explicit one-loop effective actions in N=4 SYM and N=2 SU(2) SYM with hypermultiplets.

Manifestly N=2 superconformal form of the effective actions.

Insights into supergravity-gauge theory duality and D-brane interactions.

Abstract

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.