Bootstrapping Mirror Pairs: The Beginning of the End
Leyi Jiang, Jazz E. Z. Ooi, Richard Stone, Zhenghao Zhong
TL;DR
The work tackles the challenge of mapping 3d mirror symmetry landscapes beyond brane constructions by introducing Growth and Fusion, the final piece of a quartet of quiver Higgsing algorithms (with Subtraction, Addition, and Decay/Fission). This brane-free framework enables systematic bootstrapping of new mirror pairs from known ones and is demonstrated on circular and Sunshine quivers, including non-linear sunshines and glueing constructions, with cross-checks via Higgs/Coulomb branch data and Hilbert series. The key contributions are the formalization of Growth and Fusion, the development of Sunshine quivers and the glueing method, and the demonstration that these tools can generate a broad class of Lagrangian 3d mirrors without brane setups, while also identifying limitations in cases involving special unitary components. The approach has potential to automate discovery of large swaths of the 3d mirror landscape and to connect abelian and non-abelian families, with practical implications for computing Coulomb and Higgs branch data and for aligning with other mirror-programs.
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 instalment, 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.