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Paper   IPM / Physic / 7797
School of Physics
  Title:   Integrable Spin Chains on the Conformal Moose: \cN = 1 Superconformal Gauge Theories as Six-Dimensional String Theories
1.  D. Sadri
2.  M.M. Sheikh-Jabbari
3.  S. Thomas
  Status:   Published
  Journal: JHEP
  Vol.:  03
  Year:  2006
  Pages:   024
  Supported by:  IPM
We consider \cN = 1,  D=4 superconformal SU(N)p ×q Yang-Mills theories dual to  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 three-dimensional statistical mechanical 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 a generalization of the SO(6) spin chain picture of \cN = 4 super Yang-Mills theory. We comment on the integrability of this \cN = 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.

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