Gravity Duals of Supersymmetric SU(N) x SU(N+M) Gauge Theories
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The world volume theory on N regular and M fractional D3-branes at the conifold singularity is a non-conformal n=1 supersymmetric SU(N+M) x SU(N) gauge theory. In previous work the Type IIB supergravity dual of this theory was constructed to leading non-trivial order in M/N: it is the AdS_5 x T^{1,1} background with NS-NS and R-R 2-form fields turned on. Far in the UV this dual description was shown to reproduce the logarithmic flow of couplings found in the field theory. In this paper we study the supersymmetric RG flow at all scales. We introduce an ansatz for the 10-d metric and other fields and show that the equations of motion may be derived in first order form from a simple superpotential. This allows us to explicitly solve for the gravity dual of the RG trajectory.
19 pages, harvmac; v2: a section added on the full 3-brane solution (it looks like the conventional 3-brane solution with a logarithmically running effective charge), references added
19 pages, harvmac; v2: a section added on the full 3-brane solution (it looks like the conventional 3-brane solution with a logarithmically running effective charge), references added