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A trio of dualities: walls, trees and cascades
Author(s) -
Franco S.,
Hanany A.,
He Y.H.
Publication year - 2004
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200310142
Subject(s) - duality (order theory) , gauge theory , flow (mathematics) , seiberg duality , cascade , limit (mathematics) , physics , gauge (firearms) , markov chain , finite volume method , theoretical physics , mathematics , pure mathematics , mathematical physics , mathematical analysis , supersymmetric gauge theory , quantum mechanics , geometry , chemistry , gauge anomaly , archaeology , statistics , chromatography , history
We study the RG flow of = 1 world‐volume gauge theories of D3‐brane probes on certain singular Calabi‐Yau threefolds. Taking the gauge theories out of conformality by introducing fractional branes, we compute the NSVZ beta‐function and follow the subsequent RG flow in the cascading manner of Klebanov‐Strassler. We study the duality trees that blossom from various Seiberg dualities and encode possible cascades. We observe the appearance of duality walls, a finite limit energy scale in the UV beyond which the dualization cascade cannot proceed. Diophantine equations of the Markov type characterize the dual phases of these theories. We discuss how the classification of Markov equations for different geometries into families relates the RG flows of the corresponding gauge theories.