Abstract
We examine how the Einstein-Hilbert action is renormalized by adding the usual counterterms and additional corner counterterms when the boundary surface has corners. A bulk geometry asymptotic to Hd+1 can have boundaries Sk× Hd−k and corners for 0 ≤ k < d. We show that the conformal anomaly when d is even is independent of k. When d is odd the renormalized action is a finite term that we show is independent of k when k is also odd. When k is even we were unable to extract the finite term using the counterterm method and we address this problem using instead the Kounterterm method. We also compute the mass of a two-charged black hole in AdS7 and show that background subtraction agrees with counterterm renormalization only if we use the infinite series expansion for the counterterm.
Highlights
The AdS-CFT correspondence relates Einstein gravity in the bulk with a conformal field theory on the boundary
When d is odd the renormalized action is a finite term that we show is independent of k when k is odd
We compute the mass of a two-charged black hole in AdS7 and show that background subtraction agrees with counterterm renormalization only if we use the infinite series expansion for the counterterm
Summary
The AdS-CFT correspondence relates Einstein gravity in the bulk with a conformal field theory on the boundary. If the boundary is viewed as a regulator surface near infinity, we may subtract the divergent terms in the on-shell action by adding a counterterm [16,17,18]. The on-shell value is a function of the boundary metric, I = I(hμν) To this action, one may add a boundary term that only depends on the boundary metric and its tangential derivatives without affecting the bulk equations of motion. One may add a boundary term that only depends on the boundary metric and its tangential derivatives without affecting the bulk equations of motion This can be used to construct a counterterm action [16,17,18]1. There are two figures that we placed at the end of the paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
