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arXiv · 1107.4101

Invariants of Toric Seiberg Duality

Amihay Hanany·Yang-Hui He·Vishnu Jejjala·Jurgis Pasukonis·Sanjaye Ramgoolam·Diego Rodriguez-Gomez
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Abstract

Three-branes at a given toric Calabi-Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description in terms of bipartite graphs on a torus, we find a new invariant under Seiberg duality, namely the Klein j-invariant of the complex structure parameter in the distinguished isoradial embedding of the dimer, determined by the physical R-charges. Additional number theoretic invariants are described in terms of the algebraic number field of the R-charges. We also give a new compact description of the a-maximization procedure by introducing a generalized incidence matrix.

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Amihay Hanany, Yang-Hui He, Vishnu Jejjala, Jurgis Pasukonis, Sanjaye Ramgoolam, Diego Rodriguez-Gomez. 2011-07-20. Invariants of Toric Seiberg Duality. https://doi.org/10.1142/s0217751x12500029

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