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.

Publication Type:	Article
Additional Information:	Electronic version of an article published as International Journal of Modern Physics A, Volume 27, Issue 01, 10 January 2012, 1250002, http://dx.doi.org/10.1142/S0217751X12500029 © copyright World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/ijmpa
Publisher Keywords:	Supersymmetry and duality; supersymmetric gauge theory
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics

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