Mutations vs. Seiberg duality

Vitória, Jorge

2009-01-01

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Abstract

For a quiver with potential, Derksen, Weyman and Zelevinsky defined in [H. Derksen, J. Weyman, A. Zelevinsky, Quivers with potentials and their representations I: Mutations, arXiv: 0704.0649v2 [math.RA]] a combinatorial transformation, mutations. Mukhopadhyay and Ray, on the other hand, tell us how to compute Seiberg dual quivers for some quivers with potentials through a tilting procedure, thus obtaining derived equivalent algebras. In this text, we compare mutations with the concept of Seiberg duality given by [S. Mukhopadhyay, K. Ray, Seiberg duality as derived equivalence for some quiver gauge theories, arXiv: hep-th/0309191v2], concluding that for a certain class of potentials (the good ones) mutations coincide with Seiberg duality, therefore giving derived equivalences.