Black hole partition functions and duality
By G. Cardoso, B. Wit, J. Kappeli, T. Mohaupt. 2006
133 citations recorded by the source corpus.
The macroscopic entropy and the attractor equations for BPS black holes in four-dimensional N = 2 supergravity theories follow from a variational principle for a certain `entropy function'. We present this function in the presence of R2-interactions and non-holomorphic corrections. The variational principle identifies the entropy as a Legendre transform and this motivates the definition of various partition functions corresponding to different ensembles and a hierarchy of corresponding duality invariant inverse Laplace integral representations for the microscopic degeneracies. Whenever the microscopic degeneracies are known the partition functions can be evaluated directly. This is the case for N = 4 heterotic CHL black holes, where we demonstrate that the partition functions are consistent with the results obtained on the macroscopic side for black holes that have a non-vanishing classical area. In this way we confirm the presence of a measure in the duality invariant inverse Laplace integrals. Most, but not all, of these results are obtained in the context of semiclassical approximations. For black holes whose area vanishes classically, there remain discrepancies at the semiclassical level and beyond, the nature of which is not fully understood at present.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f8ec2109563297933d2edba7d6059b8b86e0b640
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Citations in the corpus
- Lectures on black holes, topological strings and quantum attractors (2006, background): “20) has been proposed in [42], which involves an integral over both X and X̄ , or equivalently a thermodynamical ensemble with fixed electric and magnetic potentials (see Exercice 7 on page 21).”
- Quantum black holes, localization, and the topological string (2010, background): “y in an essential way. 3. It has been pointed out that agreement with statistical entropy requires modifying the OSV conjecture by including additional measure factors and nonperturbative corrections [24, 25, 26, 27, 28, 29]. Our localizing solution provides a well-defined starting point to define the”
- Black Holes, Qubits and Octonions (2008, unknown): “See also [142, 143, 144, 145, 146, 147].”
- Product representation of dyon partition function in CHL models (2006, result): “Furthermore it generates integer results for the degeneracies and its behaviour for large charges is consistent with the black hole entropy calculation[7, 19].”
- Quantum Entropy Function from AdS(2)/CFT(1) Correspondence (2008, background): “Some of these corrections are in fact necessary for restoring the duality invariance of the final result for the entropy [51,52].”
- Split states, entropy enigmas, holes and halos (2007, background): “Finally, the need for an additional measure factor was was pointed out in [12] for small black holes, in [13] for T 6 and T 2 ×K3 compactifications, in [15] for N = 4 models, and on general theoretical grounds in [20].”
- Black hole entropy function, attractors and precision counting of microstates (2007, methodology): “Our analysis will follow the one given in [6]; this in turn is based on the earlier analysis of [9, 18, 10, 173].”
- Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates (2011, methodology): “In contrast [29, 98] started from a different perspective, using symplectic invariance as the basic principle.”