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  • Open Access

Bootstrapping mirror pairs: The beginning of the end

Leyi Jiang*,†, Jazz E. Z. Ooi‡,§, Richard Stone║, and Zhenghao Zhong¶,**

  • Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, United Kingdom

  • *Contact author: ljiang@mpi-cbg.de
  • †Present address: Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG), Pfotenhauerstraße 108, 01307 Dresden, Germany; Center for Systems Biology Dresden (CSBD), Pfotenhauerstraße 108, 01307 Dresden, Germany; Faculty of Mathematics, Technische Universität Dresden, Helmholtzstraße 10, 01069 Dresden, Germany.
  • ‡Contact author: jazzooi21@gmail.com
  • §Present address: Centre for Quantum Technologies (CQT), National University of Singapore, Block S15, 3 Science Drive 2, Singapore 117543.
  • ║Contact author: richstone052@gmail.com
  • Contact author: zhong@simis.cn
  • **Present address: Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS), Block A, International Innovation Plaza, No. 657 Songhu Road, Shanghai, People’s Republic of China.
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Phys. Rev. D 113, 126013 – Published 15 June, 2026

DOI: https://doi.org/10.1103/lp73-h6j4

Abstract

Three-dimensional supersymmetric gauge theories with eight supercharges possess a unique duality known as 3D mirror symmetry. Under this correspondence, the Coulomb branch of one theory is equivalent to the Higgs branch of its mirror dual, and vice versa. Over the past decades, extensive effort has been devoted to charting the landscape of 3D mirror pairs, though progress has often been constrained by the need to identify suitable brane configurations. In this first installment, we introduce a new quiver-based algorithm, termed growth and fusion, which completes a quartet of Higgsing algorithms alongside decay and fission, quiver subtraction, and quiver addition. Together, these four algorithms provide a systematic framework that circumvents the limitations of brane constructions, enabling us to determine the mirror dual of a given quiver and to systematically bootstrap new 3D mirror pairs. We demonstrate the power of this approach on a new class of circular 3D mirror pairs.

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Phys. Rev. D 113, 126013– Published 15 June, 2026
  • Received 21 November 2025
  • Accepted 26 March 2026
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