# Quantum entropy function from AdS/CFT?

+ 3 like - 0 dislike
104 views

My question is about the AdS/CFT correspondence's place in calculating Sen's quantum entropy functions. In 2008 Sen gave a way to calculate the exact entropy of certain supersymmetric quantum black holes. In particular extremal RN black holes in 4D. Those are asymptotically isometric to $AdS^2\times S^2$. It is a development on Wald's calculation for classical gravity theories with higher derivatives in their lagrangian. The crux is caculating the expectation of a -regularized- boundary Wilson line in the quantized bulk gravity on the near-horizon $AdS^2\times S^2$. He seems to be using the AdS$^2$/CFT$^1$ correspondence but I cannot really see where.

Later articles by Dabholkar, Gomes, Murthy, et al. used localization to compute the bulk functional integral exactly as a finite dimensional integral, following Banerjee et al. But there the functional integral is over bulk fields -vector multiplets, hypermultiplets, Weyl multiplet. I cannot see where the AdS/CFT correspondence enters. Is it just a matter of taking certain limits on couplings without really considering the boundary CFT?

Furthermore if the AdS/CFT correspondence enters does it make sense to speak of a macroscopic calculation of the entropy, because passing to the boundary CFT is essentially passing (modulo a few "passage to the limit"s in between) to the brane worldvolume theory, which represents the microscopic degrees of freedom of string theory? So the quantum entropy function would better be called a different microscopic calculation of the straightforward original logarithm of the brane partition function. If this were the case would it not be better to speak of entropy computed in different frames (the weakly coupled IIB string frame near the horizon, the weakly coupled large N IIB brane frame, etc.)? It is not always a microscopic calculation if 1 passes by brane theories? I would believe macroscopic refers to spacetime string fields, entering lagrangians with arbitrarily high derivatives.

I am a little puzzled so any comment may enlighten me. Sorry if I wrote nonsense.

Main reference: arXiv:0805.0095, arXiv:0905.2686arXiv:1012.0265arXiv:1111.1161.

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOv$\varnothing$rflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.