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We consider N=1, D=4 superconformal U(N)^{pq} Yang-Mills theories dual toAdS_5xS^5/Z_pxZ_q orbifolds. We construct the dilatation operator of thissuperconformal gauge theory at one-loop planar level. We demonstrate that aspecific sector of this dilatation operator can be thought of as the transfermatrix for a two-dimensional statistical mechanical system, related to anintegrable SU(3) anti-ferromagnetic spin chain system, which in turn isequivalent to a 2+1-dimensional string theory where the spatial slices arediscretized on a triangular lattice. This is an extension of the SO(6) spinchain picture of N=4 super Yang-Mills theory. We comment on the integrabilityof this N=1 gauge theory and hence the corresponding three-dimensionalstatistical mechanical system, its connection to three-dimensional latticegauge theories, extensions to six-dimensional string theories, AdS/CFT typedualities and finally their construction via orbifolds and brane-box models. Inthe process we discover a new class of almost-BPS BMN type operators with largeengineering dimensions but controllably small anomalous corrections.Comment: 53 pages, 14 eps figures; Added reference

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