"AdS/CFT and local renormalization group with gauge fields"


Ken Kikuchi (Nagoya Univ.)


We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a (d+1)-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG equation by working with the Hamilton-Jacobi formulation of the bulk theory. The Gauss's law constraint associated with gauge symmetry plays an important role. RG flows of the background gauge fields are governed by vector beta-functions, and some interesting properties of them are known to follow. We give a systematic rederivation of them on the basis of the HJ formulation. Fixing an ambiguity of local counterterms in such a manner that is natural from the viewpoint of the HJ formulation, we determine all the coefficients uniquely appearing in the trace of the stress tensor for d=4. A relation between a choice of schemes and a Virial current is discussed. As a consistency check, these are found to satisfy the integrability conditions of local RG transformations. From these results, we are led to a proof of a holographic c-theorem by finding out a full family of schemes where a trace anomaly coefficient is related with a holographic c-function.
This presentation is based on the paper arXiv:1511.00403[hep-th].

Designed by CSS.Design Sample