Non-Abelian Finite Gauge Theories

Abstract

We study orbifolds of $\mathcal{N}=4$ U(n) super-Yang-Mills theory given by discrete subgroups of SU(2) and SU(3). We have reached many interesting observations that have graph-theoretic interpretations. For the subgroups of SU(2), we have shown how the matter content agrees with current quiver theories and have offered a possible explanation. In the case of SU(3) we have constructed a catalogue of candidates for finite (chiral) $\mathcal{N}=1$ theories, giving the gauge group and matter content. Finally, we conjecture a McKay-type correspondence for Gorenstein singularities in dimension 3 with modular invariants of WZW conformal models. This implies a connection between a class of finite $\mathcal{N}=1$ supersymmetric gauge theories in four dimensions and the classification of affine SU(3) modular invariant partition functions in two dimensions.

28 pages, 5 figs, 1 ref added, 1 table updated and some comments on binary dihedral groups added

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