Open AccessSeiberg duality as derived equivalence for some quiver gauge theories
Author(s) -
S. Mukhopadhyay,
Koushik Ray
Publication year - 2004
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2004/02/070
Subject(s) - quiver , seiberg duality , superpotential , endomorphism , mathematics , duality (order theory) , pure mathematics , equivalence (formal languages) , gauge theory , homomorphism , flatness (cosmology) , path (computing) , algebra over a field , representation theory , supersymmetric gauge theory , physics , mathematical physics , computer science , supersymmetry , quantum mechanics , gauge anomaly , cosmology , programming language
We study Seiberg duality of quiver gauge theories associated to the complexcone over the second del Pezzo surface. Homomorphisms in the path algebra ofthe quivers in each of these cases satisfy relations which follow from asuperpotential of the corresponding gauge theory as F-flatness conditions. Weverify that Seiberg duality between each pair of these theories can beunderstood as a derived equivalence between the categories of modules ofrepresentation of the path algebras of the quivers. Starting from theprojective modules of one quiver we construct tilting complexes whoseendomorphism algebra yields the path algebra of the dual quiver. Finally, wepresent a general scheme for obtaining Seiberg dual quiver theories byconstructing quivers whose path algebras are derived equivalent. We alsodiscuss some combinatorial relations between this approach and some of theother approaches which has been used to study such dualities.Comment: 20 pages, Latex, References adde
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