Witten showed that the supergravity action for black holes in anti-de Sitter space behaves like this quantity in the dual field theory, where at high temperatures conformal invariance dictates that it scales as temperature to the fourth.
Witten showed that the supergravity action for black holes in anti-de Sitter space behaves like this quantity in the dual field theory, where at high temperatures conformal invariance dictates that it scales as temperature to the fourth. One obtains it by a Legendre transformation, after which the entropy is now realized as the negative partial derivative of it with respect to temperature. It is given by - T log Z, where Z is the canonical partition function. It is equal to E minus T S. FTP, what is this thermodynamic quantity, differing from the similarly named Gibbs quantity by a PV term?
Witten showed that the supergravity action for black holes in anti-de Sitter space behaves like this quantity in the dual field theory, where at high temperatures conformal invariance dictates that it scales as temperature to the fourth.
Helmholtz free energy (prompt on "free energy," until "Gibbs")