paper

A Trio of Dualities: Walls, Trees and Cascades

arXiv:hep-th/0312222 · doi:10.1002/prop.200310142

Abstract

We study the RG flow of N=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.

arXiv comment10 pages, 13 figures, Submitted to "Fortschritte der Physik" as part of the proceedings of the "36th International Symposium Ahrenshoop on the Theory of Elementary Particles," Berlin, August 26-30, 2003, and based on talks given by A. Hanany in Berlin and The University of Pennsylvannia, Philadelphia

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