BPS quivers and spectra of complete \(\mathcal N =2\) quantum field theories. (English) Zbl 1305.81118
Summary: We study the BPS spectra of \(\mathcal N = 2\) complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and superpotential for the theory. The BPS spectrum can then be determined by solving the quantum mechanics problem encoded by the quiver. By analyzing the structure of this quantum mechanics we show that all asymptotically free examples, Argyres-Douglas models, and theories defined by punctured spheres and tori have a chamber with finitely many BPS states. In all such cases we determine the spectrum.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 16G70 | Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 16G20 | Representations of quivers and partially ordered sets |
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