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Title of Journal: J High Energ Phys

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Abbravation: Journal of High Energy Physics

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Springer Berlin Heidelberg

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DOI

10.1007/s00362-002-0116-9

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1029-8479

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Sduality triangle groups and modular anomalies i

Authors: S K Ashok E Dell’Aquila A Lerda M Raman
Publish Date: 2016/04/19
Volume: 2016, Issue: 4, Pages: 118-
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Abstract

We study mathcalN=2 superconformal theories with gauge group SUN and 2N fundamental flavours in a locus of the Coulomb branch with a mathbbZ N symmetry In this special vacuum we calculate the prepotential the dual periods and the period matrixusing equivariant localization When the flavors are massless we find that the period matrix is completely specified by leftfracN2right effective couplings On each of these we show that the Sduality group acts as a generalized triangle group and that its hauptmodul can be used to write a nonperturbatively exact relation between each effective coupling and the bare one For N = 2 3 4 and 6 the generalized triangle group is an arithmetic Hecke group which contains a subgroup that is also a congruence subgroup of the modular group mathrmPmathrmSmathrmLleft2mathbbZright For these cases we introduce mass deformations that respect the symmetries of the special vacuum and show that the constraints arising from Sduality make it possible to resum the instanton contributions to the period matrix in terms of meromorphic modular forms which solve modular anomaly equationsThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team

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