Skip to main content
Entropy bounds, monotonicity properties and scaling in CFTs
Nuclear Physics B (2001)
  • D. Klemm
  • A.C. Petkou
  • George Siopsis, University of Tennessee, Knoxville

We study the ratio of the entropy to the total energy in conformal field theories at finite temperature. For the free field realizations of N=4 source super Yang–Mills theory in D=4 and the (2,0) tensor multiplet in D=6, the ratio is bounded from above. The corresponding bounds are less stringent than the recently proposed Verlinde bound. We show that entropy bounds arise generically in CFTs in connection to monotonicity properties with respect to temperature changes of a generalized C-function. For strongly coupled CFTs with AdS duals, we show that the ratio obeys the Verlinde bound even in the presence of rotation. For such CFTs, we point out an intriguing resemblance in their thermodynamic formulas with the corresponding ones of two-dimensional CFTs. We show that simple scaling forms for the free energy and entropy of CFTs with AdS duals reproduce the thermodynamical properties of (D+1)-dimensional AdS black holes.


  • Cardy–Verlinde,
  • entropy,
  • black holes,
  • conformal field theories
Publication Date
May 7, 2001
Citation Information
D. Klemm, A.C. Petkou and George Siopsis. "Entropy bounds, monotonicity properties and scaling in CFTs" Nuclear Physics B Vol. 601 Iss. 1-2 (2001)
Available at: