The Duality Cascade

TL;DR

This paper explains the physics of the duality cascade in string theory and gauge theories, introducing new insights into supergravity smoothness, coupling relations, and fixed points, aimed at both experts and students.

Contribution

It provides a detailed explanation of the duality cascade, including previously unpublished results on supergravity smoothness, coupling relations, and fixed points in the cascade.

Findings

Supergravity perceives the cascade as smooth.

Relation between supergravity couplings and gauge theory couplings.

Existence of twice as many approximate fixed points as expected.

Abstract

The duality cascade, and its dual description as string theory on the warped deformed conifold, brings together several sophisticated topics, some of which are not widely known. These lectures, which contain a number of previously unpublished results, and are intended for experts as well as students, seek to explain the physics of duality cascades. Seiberg duality is carefully introduced, with detailed attention to the physical implications of duality away from the far infrared. The conifold is briefly introduced and strings on the conifold (the Klebanov-Witten model) are discussed. Next, fractional branes are introduced. The duality cascade is then constructed in field theory and in its dual supergravity description. Among the newly published results: it is shown why supergravity sees the cascade as smooth; how the two holomorphic couplings (dilaton and integrated two-form in supergravity) are related to the three physical couplings in the gauge theory; that there are actually twice as many approximate fixed points in the cascade as might be naively expected. These notes are based on lectures given at TASI 2003 and at the 2003 PIMS Summer School on Strings, Gravity & Cosmology.