Integrable spin chains on the conformal moose: Script N = 1 superconformal gauge theories as six-dimensional string theories

2005/10/31 by Darius Sadri, M. M. Sheikh-Jabbari · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Gauge theory #Geometry #Integrable system #Lattice (music) #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Spin (aerodynamics) #String (physics) #String theory #Theoretical physics #hep-th

paper · pdf · doi:10.1088/1126-6708/2006/03/024

published as JHEP 0603:024,2006 · 53 pages, 14 eps figures; Added references

arxiv created 2005/11/09 · openalex publication_date 2006/03/07 · arxiv updated 2009/12/01 · openalex created_date 2021/02/01 · openalex updated_date 2026/06/15

Abstract

We consider N=1, D=4 superconformal U(N)^pq Yang-Mills theories dual to AdS₅xS⁵/Z_pxZ_q orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector of this dilatation operator can be thought of as the transfer matrix for a two-dimensional statistical mechanical system, related to an integrable SU(3) anti-ferromagnetic spin chain system, which in turn is equivalent to a 2+1-dimensional string theory where the spatial slices are discretized on a triangular lattice. This is an extension of the SO(6) spin chain picture of N=4 super Yang-Mills theory. We comment on the integrability of this N=1 gauge theory and hence the corresponding three-dimensional statistical mechanical system, its connection to three-dimensional lattice gauge theories, extensions to six-dimensional string theories, AdS/CFT type dualities and finally their construction via orbifolds and brane-box models. In the process we discover a new class of almost-BPS BMN type operators with large engineering dimensions but controllably small anomalous corrections.

Citations

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• D-branes, Quivers, and ALE Instantons
• The dilatation operator of N=4 super Yang–Mills theory and integrability
• The large N limit of superconformal field theories and supergravity

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• Phases of thermal 𝒩 = 2 quiver gauge theories