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Higgs branch RG flows via decay and fission

Antoine Bourget1,*, Marcus Sperling2,†, and Zhenghao Zhong3,‡

  • 1Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France
  • 2Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
  • 3Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, United Kingdom

  • *antoine.bourget@ipht.fr
  • †marcus.sperling@univie.ac.at
  • ‡zhenghao.zhong@maths.ox.ac.uk
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Phys. Rev. D 109, 126013 – Published 21 June, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.126013

Abstract

Magnetic quivers have been an instrumental technique for advancing our understanding of Higgs branches of supersymmetric theories with eight supercharges. In this work, we present the “decay and fission” algorithm for unitary magnetic quivers. It enables the derivation of the complete phase (Hasse) diagram and is characterized by the following key attributes: First and foremost, the algorithm is inherently simple, just relying on convex linear algebra. Second, any magnetic quiver can only undergo decay or fission processes; these reflect the possible Higgs branch RG flows (Higgsings), and the quivers thereby generated are the magnetic quivers of the new RG fixed points. Third, the geometry of the decay or fission transition (i.e., the transverse slice) is simply read off. As a consequence, the algorithm does not rely on a complete list of minimal transitions, but rather outputs the transverse slice geometry automatically. As a proof of concept, its efficacy is showcased across various scenarios, encompassing superconformal field theories from dimensions 3 to 6, instanton moduli spaces, and little string theories.

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Phys. Rev. D 109, 126013– Published 21 June, 2024
  • Received 22 February 2024
  • Accepted 8 April 2024
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