4d N=2 Gauge Theories and Quivers: the Non-Simply Laced Case

TL;DR

This paper constructs BPS quivers with superpotential for 4d N=2 gauge theories with non-simply laced Lie groups, extending geometric and categorical methods to these cases.

Contribution

It introduces a novel construction of BPS quivers for non-simply laced gauge groups using geometric engineering and categorical techniques, including a new specialization method.

Findings

Constructed BPS quivers for B_n, C_n, F_4, G_2 gauge theories.

Extended geometric engineering to non-simply laced cases.

Proposed a specialization method for matter representations.

Abstract

We construct the BPS quivers with superpotential for the 4d N=2 gauge theories with non-simply laced Lie groups (B_n, C_n, F_4 and G_2). The construction is inspired by the BIKMSV geometric engineering of these gauge groups as non-split singular elliptic fibrations. From the categorical viewpoint of arXiv:1203.6743, the fibration of the light category L(g) over the (degenerate) Gaiotto curve has a monodromy given by the action of the outer automorphism of the corresponding unfolded Lie algebra. In view of the Katz--Vafa `matter from geometry' mechanism, the monodromic idea may be extended to the construction of (Q, W) for SYM coupled to higher matter representations. This is done through a construction we call specialization.