Two years ago, Antoine Bourget (Université Paris-Saclay), Marcus Sperling (Faculty of Physics, University of Vienna) and Zhenghao Zhong described in the journal Physical Review Letters how so-called magnetic quivers can decay and split, much like radioactive atomic nuclei. Magnetic quivers are a graphical tool for describing supersymmetric quantum field theories - simplified model systems that serve as a theoretical laboratory for the foundations of particle physics. Now comes the sequel: a team from Vienna and Paris-Saclay has systematically investigated which quivers do not decay any further. These stable building blocks form, in a sense, a "periodic table" for a large class of supersymmetric quantum field theories. Among them are three new families, two of which provide new examples of a rare class of geometric objects. The paper was published on 7 September in Annales Henri Poincaré.
Magnetic quivers consist of nodes and lines that represent quantum fields and their interactions. They describe the ground states of these theories, the so-called vacua. In this language, the Higgs mechanism - which in the Standard Model gives elementary particles their mass - can be read as a chain of decays and fissions: a complex quiver decays step by step into simpler ones until only stable quivers remain. Just as every molecule is composed of the elements of the periodic table, every Higgs mechanism is composed of these elementary steps. The stable quivers are thus the true building blocks.
On the basis of the so-called decay-and-fission conjecture, the team has now compiled the complete list of stable quivers in this class. Remarkably, the previously known examples among them - some originating from entirely different mathematical constructions - all reappear here in a single unified language. In addition, there are three new infinite families of stable quivers. One of them provides a new description of already known objects, while the other two yield previously unknown examples of so-called isolated symplectic singularities. Since the French mathematician Arnaud Beauville asked for further examples of such structures in 1999, the list has grown only slowly.
The work shows that the exchange between physics and mathematics works in both directions: here, a physically motivated algorithm delivers new results for mathematics. At the same time, the team points out that the completeness of the list depends on the decay-and-fission conjecture. Also still open is a rigorous proof that the new families possess the additional property Beauville had asked for - a trivial local fundamental group. If they do, they would be new answers to his question.
A substantial part of the work stems from the doctoral thesis of Sinan Moura Soysüren, who completed his PhD at the University of Vienna within the FWF-funded START project of Marcus Sperling and will shortly take up his first postdoctoral position. The other authors are Antoine Bourget of Université Paris-Saclay, who was already involved in the 2024 paper, and his doctoral student Quentin Lamouret.
Original publication: Antoine Bourget, Quentin Lamouret, Sinan Moura Soysüren, Marcus Sperling: Classifying Isolated Symplectic Singularities via 3d N=4 Coulomb Branches. Annales Henri Poincaré (2026). DOI: 10.1007/s00023-026-01732-w. Free-to-read version: https://rdcu.be/5vdofD7T2BHa
Previous publication: Antoine Bourget, Marcus Sperling, Zhenghao Zhong: Decay and Fission of Magnetic Quivers. Physical Review Letters 132, 221603 (2024). DOI: 10.1103/PhysRevLett.132.221603
Funding: FWF START project "Phases of Quantum Field Theories: Symmetries and Vacua" (quiverQFT), DOI: 10.55776/STA73. Additional support was provided by the Vienna Doctoral School in Physics and the Faculty of Physics of the University of Vienna.
