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Exact WKB analysis of N = 2 gauge theories

Research paper by Sujay K. Ashok, Dileep P. Jatkar, Renjan R. John, M. Raman, Jan Troost

Indexed on: 21 Jul '16Published on: 21 Jul '16Published in: Journal of High Energy Physics



Abstract

We study \( \mathcal{N} \) = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations satisfied by ϵ1- and ϵ2-deformed instanton partition functions. We confirm their validity at leading order in ϵ2 via a saddle-point analysis of the partition function. In the semi-classical limit we show that these differential equations take a form amenable to exact WKB analysis. We compute the monodromy group associated to the differential equations in terms of ϵ1-deformed and Borel resummed Seiberg-Witten data. For each case, we study pairs of Stokes graphs that are related by flips and pops, and show that the monodromy groups allow one to confirm the Stokes automorphisms that arise as the phase of ϵ1 is varied. Finally, we relate the Borel resummed monodromies with the traditional Seiberg-Witten variables in the semi-classical limit.