Holography without counter terms

TL;DR

This paper derives a unified Smarr-like relation for AdS black holes using scaling behavior, enabling holographic renormalization without explicit counter terms, which benefits condensed matter applications via AdS/CMT.

Contribution

It introduces a novel method to obtain holographically renormalized actions without explicit counter terms, simplifying calculations in holography.

Findings

Consistent results with existing models

Provides an efficient holographic renormalization technique

Offers new insights into AdS/CMT applications

Abstract

By considering the behavior of the reduced action under the scaling transformation, we present a unified derivation of the Smarr-like relation for asymptotically anti-de-Sitter planar black holes. This novel Smarr-like relation leads to useful information in the condensed matter systems through the AdS/CMT correspondence. By using our results, we provide an efficient way to obtain the holographically renormalized on-shell action without the information on the explicit forms of counter terms. We find the complete consistency of our results with those in various models discussed in the recent literatures and obtain new implications.