Monopole and Dyon Spectra in N=2 SYM with Higher Rank Gauge Groups

TL;DR

This paper analyzes monopole and dyon spectra in N=2 super-Yang--Mills theories with higher rank gauge groups, highlighting complexities in duality interpretations and focusing on specific cases like G=SU(3).

Contribution

It derives monopole and dyon spectra for N=2 SYM theories with higher rank gauge groups and discusses the implications for duality and finiteness.

Findings

Standard dyon spectrum procedures may not support selfduality hypotheses.

SU(2) with four hypermultiplets may be an exception to duality expectations.

Spectra are derived for theories with finite matter content.

Abstract

We derive parts of the monopole and dyon spectra for N=2 super-Yang--Mills theories in four dimensions with gauge groups G of rank r>1 and matter multiplets. Special emphasis is put on G=SU(3) and those matter contents that yield perturbatively finite theories. There is no direct interpretation of the soliton spectra in terms of naive selfduality under strong--weak coupling and exchange of electric and magnetic charges. We argue that, in general, the standard procedure of finding the dyon spectrum will not give results that support a conventional selfduality hypothesis --- the SU(2) theory with four fundamental hypermultiplets seems to be an exception. Possible interpretations of the results are discussed.