Seiberg duality as derived equivalence for some quiver gauge theories

Abstract

We study Seiberg duality of quiver gauge theories associated to the complex cone over the second del Pezzo surface. Homomorphisms in the path algebra of the quivers in each of these cases satisfy relations which follow from a superpotential of the corresponding gauge theory as F-flatness conditions. We verify that Seiberg duality between each pair of these theories can be understood as a derived equivalence between the categories of modules of representation of the path algebras of the quivers. Starting from the projective modules of one quiver we construct tilting complexes whose endomorphism algebra yields the path algebra of the dual quiver. Finally, we present a general scheme for obtaining Seiberg dual quiver theories by constructing quivers whose path algebras are derived equivalent. We also discuss some combinatorial relations between this approach and some of the other approaches which has been used to study such dualities.

20 pages, Latex, References added

References in corpus (4)

• Unhiggsing the del Pezzo
• On Berenstein-Douglas-Seiberg Duality
• On Duality Walls in String Theory
• Toric Duality, Seiberg Duality and Picard-Lefschetz Transformations

Cited by in corpus (12)

• Brane Tilings and Their Applications
• Seiberg Duality is an Exceptional Mutation
• Exceptional Collections and del Pezzo Gauge Theories
• Cluster mutation-periodic quivers and associated Laurent sequences
• The Coulomb Branch Formula for Quiver Moduli Spaces
• Kaluza-Klein Type Robertson Walker Cosmological Model With Dynamical Cosmological Term $\Lambda$
• Quiver Gauge Theory and Conformality at the TeV Scale
• Generalized quiver mutations and single-centered indices
• Mutation of frozen Jacobian algebras
• Seiberg duality for Chern-Simons quivers and D-brane mutations
• Remarks on quiver gauge theories from open topological string theory
• Effect of Dynamical Cosmological Constant in presence of Modified Chaplygin Gas for Accelerating Universe