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Invariants of Toric Seiberg Duality

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arxiv 1107.4101 v1 pith:T4OGCB7R submitted 2011-07-20 hep-th math-phmath.MPmath.NT

Amihay Hanany , Yang-Hui He , Vishnu Jejjala , Jurgis Pasukonis , Sanjaye Ramgoolam , Diego Rodriguez-Gomez This is my paper · ORCID
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keywords dualityseibergtoricdescriptiondimerfieldinvariantsnumber
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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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  1. Metaheuristic Generation of Brane Tilings

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    Simulated annealing over permutation tuples can generate consistent brane tilings, yielding a 26-field example not present in catalogues that stop at 24 fields.

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