Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-09-18
JHEP 0402 (2004) 070
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, Latex, References added
Scientific paper
10.1088/1126-6708/2004/02/070
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.
Mukhopadhyay Subir
Ray Koushik
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