Holographic Renormalization of Probe D-Branes in AdS/CFT

TL;DR

This paper develops a holographic renormalization procedure for probe D-branes in AdS_5 x S^5, identifying universal counterterms and scheme-dependent finite terms, enhancing understanding of D-brane dynamics in AdS/CFT.

Contribution

It provides explicit counterterms for four types of probe D-branes in AdS/CFT, showing their universality and the role of supersymmetry in fixing scheme-dependent terms.

Findings

Counterterms match those for free massive scalars in AdS_m.

Finite counterterms depend on scheme and can be fixed by supersymmetry.

Results apply to D7, D5, and D3 probe branes in AdS/CFT.

Abstract

We perform holographic renormalization for probe branes in AdS_5 x S^5. We show that for four known probe D-branes wrapping an AdS_m x S^n, the counterterms needed to render the action finite are identical to those for the free, massive scalar in AdS_m plus counterterms for the renormalization of the volume of AdS_m. The four cases we consider are the probe D7, two different probe D5's and a probe D3. In the D7 case there are scheme-dependent finite counterterms that can be fixed by supersymmetry.