Integrable Spin Chains on the Conformal Moose

Abstract

We consider N=1, D=4 superconformal U(N)^{pq} Yang-Mills theories dual to AdS_5xS^5/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.

53 pages, 14 eps figures; Added references

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Cited by in corpus (8)

• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• Emergent geometry from q-deformations of N=4 super Yang-Mills
• Aspects of emergent geometry in the AdS/CFT context
• Bethe Ansatz Equations for General Orbifolds of N=4 SYM
• Quiver gauge theories and integrable lattice models
• Deconstructing the Little Hagedorn Holography
• On the pp-wave limit and the BMN structure of new Sasaki-Einstein spaces
• Phases of Thermal N=2 Quiver Gauge Theories