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Irrelevant deformations and the holographic Callan-Symanzik equation

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Abstract

We discuss the systematics of obtaining the Callan-Symanzik equation within the framework of the gauge/gravity dualities. We present a completely general formula which in particular takes into account the new holographic renormalization results of [1]. Non-trivial beta functions are obtained from new logarithmic terms in the radial expansion of the fields. The appearance of multi-trace counterterms is also discussed in detail and we show that mixing between single-and multi-trace operators leads to very specific non-linearities in the Callan-Symanzik equation. Additionally, we compute the conformal anomaly for a scalar three-point function in a CFT.

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  1. C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY, 11794-3840, U.S.A.

    Balt C. van Rees

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van Rees, B.C. Irrelevant deformations and the holographic Callan-Symanzik equation. J. High Energ. Phys. 2011, 67 (2011). https://doi.org/10.1007/JHEP10(2011)067

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