Open AccessQuiver theories, soliton spectra and Picard-Lefschetz transformations
Author(s) -
Bo Feng,
Amihay Hanany,
YangHui He,
Amer Iqbal
Publication year - 2003
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 - 10.1088/1126-6708/2003/02/056
Subject(s) - quiver , orbifold , mathematics , dual polyhedron , mirror symmetry , pure mathematics , moduli space , duality (order theory) , polygon (computer graphics) , seiberg duality , gravitational singularity , newton polygon , simple (philosophy) , mathematical physics , gauge theory , mathematical analysis , supersymmetric gauge theory , telecommunications , philosophy , gauge anomaly , epistemology , frame (networking) , computer science
Quiver theories arising on D3-branes at orbifold and del Pezzo singularitiesare studied using mirror symmetry. We show that the quivers for the orbifoldtheories are given by the soliton spectrum of massive 2d N=2 theory withweighted projective spaces as target. For the theories obtained from the delPezzo singularities we show that the geometry of the mirror manifold givesquiver theories related to each other by Picard-Lefschetz transformations, asubset of which are simple Seiberg duals. We also address how one indeedderives Seiberg duality on the matter content from such geometrical transitionsand how one could go beyond and obtain certain ``fractional Seiberg duals.''Moreover, from the mirror geometry for the del Pezzos arise certain Diophantineequations which classify all quivers related by Picard-Lefschetz. Some of theseDiophantine equations can also be obtained from the classification results ofCecotti-Vafa for the 2d N=2 theories.Comment: 34 pages, 11 figure
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