Finite Cut-Off Holography and the DBI Counter-Term

TL;DR

This paper explores the properties of the DBI gravitational counter-term in AdS4 holography, showing it preserves certain invariances under cut-off deformations and influences entanglement entropy and RG flow.

Contribution

It introduces the DBI counter-term as a novel holographic renormalization tool that maintains invariance of key quantities under cut-off changes.

Findings

The three-sphere partition function is independent of the radial cut-off.

Renormalized entanglement entropy can be invariant under cut-off deformations.

DBI counter-term is linked to fewer degrees of freedom compared to other counter-terms.

Abstract

We demonstrate some very special features of the Dirac-Born-Infeld--like (DBI) gravitational counter-term in AdS$_4$ spacetime, in the context of holography with a sharp radial cut-off. We show that the three-sphere partition function is not only independent of a constant radial cut-off, but also remains unchanged under deformations of the cut-off surface. We also consider the renormalized holographic entanglement entropy for an equatorial Ryu-Takayanagi surface with a cut-off with an arbitrary shape and show that it can also be independent of the cut-off under a special condition. We also numerically study the behavior of the renormalized entropy with different counter-terms and relate the results to monotonicity properties under holographic renormalization group flow. The DBI counter-term is always seen to be associated with integrating out fewer degrees of freedom compared to other counter-terms.