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Paper IPM / Physic / 7797  


Abstract:  
We consider \cN = 1, D=4 superconformal SU(N)^{p ×q}
YangMills theories dual to orbifolds. We construct the
dilatation operator of this superconformal gauge theory at
oneloop, planar level. We demonstrate that a specific sector of
this dilatation operator can be thought of as the transfer matrix
for a threedimensional statistical mechanical system, which in
turn is equivalent to a 2+1dimensional 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
YangMills theory. We comment on the integrability of this \cN = 1
gauge theory and hence the corresponding threedimensional
statistical mechanical system, its connection to threedimensional
lattice gauge theories, extensions to sixdimensional string
theories, AdS/CFT type dualities and finally their construction
via orbifolds and branebox models. In the process we discover a
new class of almostBPS BMN type operators with large engineering
dimensions but controllably small anomalous corrections.
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