The dyon spectra of finite gauge theories

TL;DR

This paper proves the existence and uniqueness of all (p,q) dyon bound states in certain supersymmetric SU(2) gauge theories, establishing their duality properties and connecting to string dualities without relying on duality assumptions.

Contribution

It provides a field-theoretic proof of dyon spectra, demonstrates the presence of an exact Gamma(2) duality, and explores the spectra in massive theories and their string theory implications.

Findings

All (p,q) dyons exist and are unique in N=4 and N=2 theories.

Theories exhibit an exact Gamma(2) duality symmetry.

Massive theories' spectra align with S duality expectations.

Abstract

It is shown that all the (p,q) dyon bound states exist and are unique in N=4 and N=2 with four massless flavours supersymmetric SU(2) Yang-Mills theories, where p and q are any relatively prime integers. The proof can be understood in the context of field theory alone, and does not rely on any duality assumption. We also give a general physical argument showing that these theories should have at least an exact Gamma(2) duality symmetry, and then deduce in particular the existence of the (2p,2q) vector multiplets in the Nf=4 theory. The corresponding massive theories are studied in parallel, and it is shown that though in these cases the spectrum is no longer self-dual at a given point on the moduli space, it is still in perfect agreement with an exact S duality. We also discuss the interplay between our results and both the semiclassical quantization and the heterotic-type II string-string duality conjecture.