Invariants of Toric Seiberg Duality

Details Invariants of Toric Seiberg Duality Invariants of Toric Seiberg Duality

2011-07-20

arxiv.org/abs/1107.4101v1

Physics

High Energy Physics

High Energy Physics - Theory

43 pages, 8 figures, LaTeX

Scientific paper

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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