On the construction of $\mathcal{N}=4$ SYM effective action beyond leading low-energy approximation

Abstract

A problem of the hidden $\mathcal{N}=2$ supersymmetry deformation for next-to-leading terms in the effective action for $\mathcal{N}=4$ SYM theory is discussed. Using formulation of the theory in $\mathcal{N}=2$ harmonic superspace and exploring the on-shell hidden $\mathcal{N}=2$ supersymmetry of $\mathcal{N}=4$ SYM theory, we construct the appropriate hypermultiplet-depending contributions for $F^6$ term in the Schwinger-De Witt expansion of the effective action. The procedure involves deformed hidden $\mathcal{N}=2$ supersymmetry and allows one to obtain self-consistently the correct $\mathcal{N}=4$ supersymmetric functional containing $F^6$ among the component fields.

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