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Holographic R-symmetric flows and the τ_U conjecture

We discuss the holographic counterpart of a recent conjecture regarding R-symmetric RG-flows in four-dimensional supersymmetric field theories. In such theories, a quantity τ_U can be defined at the fixed points which was conjectured in arXiv:1109.3279 to be larger in the UV than in the IR, τ_U^{UV} > τ_U^{IR}. We analyze this conjecture from a dual supergravity perspective: using some general properties of domain wall solutions dual to R-symmetric RG flows, we define a bulk quantity which interpolates between the correct τ_U at the UV and IR fixed points, and study its monotonicity properties in a class of examples. We find a monotonic behavior for theories flowing to an interacting IR fixed point. For gapped theories, the monotonicity is still valid up to a finite value of the radial coordinate where the function vanishes, reflecting the gap scale of the field theory.