Low-energy next-to-leading contributions to the effective action in $\mathcal{N}=4$ SYM theory

Abstract

Using formulation of $\mathcal{N}=4$ SYM theory in terms of $\mathcal{N}=1$ superfields superfields we construct the derivative expansion of the one-loop $\mathcal{N}=4$ SYM effective action in background fields corresponding to constant Abelian strength $F_{mn}$ and constant hypermultiplet. Any term of the effective action derivative expansion can be rewritten in terms of $\mathcal{N}=2$ superfields. The action is manifestly $\mathcal{N}=2$ supersymmetric but on-shell hidden $\mathcal{N}=2$ supersymmetry is violated. We propose a procedure which allows to restore the hidden $\mathcal{N}=2$ invariance.

LaTeX, 6 pages, Talk given by at the International Workshop ``Supersymmetries and Quantum Symmetries'' (SQS 03), BLTP, JINR, Dubna, Russia, July 24-29, 2003