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| Paper IPM / P / 7797 |
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| Abstract: | |||||||
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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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