Abstract
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 τU can be defined at the fixed points which was conjectured in [1] to be larger in the UV than in the IR, \( \tau_U^{\mathrm{UV}}>\tau_U^{\mathrm{IR}} \). 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.
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ArXiv ePrint: 1304.1481
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Bertolini, M., Di Pietro, L. & Porri, F. Holographic R-symmetric flows and the τ U conjecture. J. High Energ. Phys. 2013, 71 (2013). https://doi.org/10.1007/JHEP08(2013)071
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DOI: https://doi.org/10.1007/JHEP08(2013)071