$S$-duality in Vafa-Witten theory for non-simply laced gauge groups

Details $S$-duality in Vafa-Witten theory for non-simply laced gauge groups $S$-duality in Vafa-Witten theory for non-simply laced gauge groups

2008-02-14

arxiv.org/abs/0802.2047v1

JHEP0805:009,2008

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1088/1126-6708/2008/05/009

Vafa-Witten theory is a twisted N=4 supersymmetric gauge theory whose partition functions are the generating functions of the Euler number of instanton moduli spaces. In this paper, we recall quantum gauge theory with discrete electric and magnetic fluxes and review the main results of Vafa-Witten theory when the gauge group is simply laced. Based on the transformations of theta functions and their appearance in the blow-up formulae, we propose explicit transformations of the partition functions under the Hecke group when the gauge group is non-simply laced. We provide various evidences and consistency checks.

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