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Cutting and gluing with running couplings in N=2 QCD

Johannes Aspman, Elias Furrer, and Jan Manschot
Phys. Rev. D 105, 025021 – Published 25 January 2022

Abstract

We consider the order parameter u=Trϕ2 as a function of the running coupling constant τH of asymptotically free N=2 QCD with gauge group SU(2) and Nf3 massive hypermultiplets. If the domain for τ is restricted to an appropriate fundamental domain FNf, then the function u is one to one. We demonstrate that these domains consist of six or less images of an SL(2,Z) keyhole fundamental domain, with appropriate identifications of the boundaries. For special choices of the masses, u does not give rise to branch points and cuts, such that u is a modular function for a congruence subgroup Γ of SL(2,Z) and the fundamental domain is Γ\H. For generic masses, however, branch points and cuts are present, and subsets of FNf are being cut and glued upon varying the mass. We study this mechanism for various phenomena, such as the decoupling of hypermultiplets, the merging of local singularities, as well as the merging of nonlocal singularities which give rise to superconformal Argyres-Douglas theories.

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  • Received 17 August 2021
  • Accepted 7 October 2021

DOI:https://doi.org/10.1103/PhysRevD.105.025021

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Johannes Aspman*, Elias Furrer, and Jan Manschot

  • School of Mathematics, Trinity College, Dublin 2, Ireland and Hamilton Mathematical Institute, Trinity College, Dublin 2, Ireland

  • *aspmanj@maths.tcd.ie
  • furrere@maths.tcd.ie
  • manschot@maths.tcd.ie

See Also

Four flavors, triality, and bimodular forms

Johannes Aspman, Elias Furrer, and Jan Manschot
Phys. Rev. D 105, 025017 (2022)

Article Text

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Vol. 105, Iss. 2 — 15 January 2022

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