Invariants of Toric Seiberg Duality

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.

43 pages, 8 figures, LaTeX

References in corpus (14)

• Dimer models and toric diagrams
• Brane Tilings
• The Master Space of N=1 Gauge Theories
• Brane Tilings and Their Applications
• An introduction to the dimer model
• Seiberg Duality for Quiver Gauge Theories
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Symmetry-breaking vacua and baryon condensates in AdS/CFT
• Deformations of Toric Singularities and Fractional Branes
• What is the Simplest Gauge-String Duality?
• Master Space, Hilbert Series and Seiberg Duality
• D-branes in non-critical superstrings and duality in N=1 gauge theories with flavor
• Emerging Non-Anomalous Baryonic Symmetries in the AdS_5/CFT_4 Correspondence
• Eulerian digraphs and toric Calabi-Yau varieties

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• Consistency and Derangements in Brane Tilings
• Composite Genus One Belyi Maps
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• Quiver Gauge Theories: Beyond Reflexivity
• Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
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