Title: A Holographic form for Wilson's RG

Speaker: Prof. Bala Sathiapalan, IMSc, Chennai

Abstract: An attempt is made to make precise the connection between Wilson's RG and ``Holographic RG'' by writing Wilson's RG in a holographic form. A functional formulation is given for the exact RG evolution of a scalar field in $d$ (flat) dimensions. It is shown that a change of variables maps the action to that for a scalar field in $AdS_{d+1}$. This provides a holographic form for Wilson's RG that can be called ``Holographic RG’’ thus making contact with the AdS-CFT conjecture. This mapping can only be done for a specific form of the cutoff function in the Exact Renormalization Group formalism. The notion of scale and conformal invariance in the presence of a {\em finite} UV cutoff is emphasized. The discussion is primarily about the two-point function and the Gaussian fixed point. Some remarks are made about nontrivial fixed points and anomalous dimensions.