Central charges, S-duality and massive vacua of N=1* super Yang-Mills

TL;DR

This paper derives the extremal superpotential values in massive vacua of N=1* super Yang-Mills using modular properties of central charges and S-duality, expressing results via Eisenstein series.

Contribution

It presents a novel derivation of vacuum superpotentials in N=1* SYM based on modular weights and S-duality, connecting superalgebra and dyon spectrum.

Findings

Exact superpotentials expressed in Eisenstein series.

Modular weight analysis determines vacuum structure.

S-duality constrains the superpotential form.

Abstract

We provide a simple derivation of the extremal values of the superpotential in massive vacua of N=1* SYM, making use of the required modular weight for the central charge of BPS walls interpolating between these vacua. This modular weight descends from the action of S-duality on the N=4 superalgebra which in turn is inherited from its classical action on the dyon spectrum. We show that this kinematic information, combined with minimal knowledge of the weak coupling asymptotics, is sufficient to determine the exact vacuum superpotentials in terms of Eisenstein series.