Arithmetic of quantum entropy function
By Ashoke Sen. 2009
171 citations recorded by the source corpus.
Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral — whose existence depends on the arithmetical properties of the black hole charges — constructed as freely acting orbifolds of the original AdS2 × S2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/57d2f5576e2566d8303f02c68f04ac8a68e8281e
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Citations in the corpus
- Near Extremal Kerr Entropy from AdS(2) Quantum Gravity (2009, unknown): “1 acastro@physics.mcgill.ca 2 larsenf@umich.edu”
- Exact microstate counting for dyonic black holes in AdS4 (2016, background): “In the near-horizon canonical ensemble this implies that all BH states have zero U (1)c charge (by an argument similar to that in [24,25]).”
- Logarithmic corrections to extremal black hole entropy from quantum entropy function (2010, background): “The rest of the contribution can be interpreted as the one loop correction to the black hole entropy [10, 50] and takes the form”
- Wall crossing from Boltzmann black hole halos (2010, background): “Similarly the (7)Since a single centered BPS black hole is expected to carry zero angular momentum[46, 47, 48], one might naively expect Ω̄+ref(γ, y) to be independent of y.”
- Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions (2011, methodology): “In order to determine this multiplicity we shall use the fact that the gravitino zero modes are associated with the deformations generated by the fermionic generators of the N = 4 superconformal algebra labelled as G n where α and β each takes value ±1 and n ∈ ZZ + 12 [30, 67].”
- Quantum black holes, localization, and the topological string (2010, background): “Based on the structure of known microscopic degeneracy formulas, it was proposed in [69, 22] that there is a universal series of saddle points to the path integral semiclassical solutions of the theory with the same boundary conditions as the pure AdS2, but which differs in the bulk.”
- Witten index and wall crossing (2014, background): “N = 2 theories, generalizing and fine-tuning Ashoke Sen’s earlier proposal to separate singe-center black holes from multi-center ones via angular momentum content [61].”
- The statistical mechanics of near-BPS black holes (2020, unknown): “For previous arguments see for example [54–56].”
- Black Holes in 4D N=4 Super-Yang-Mills Field Theory (2018, background): “Thus, when Rtrial is tuned to Rsc, the index counts the black hole states with no extra signs or phases (this is similar to [71,72]).”
- Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates (2011, background): “It was argued in [57,58] that the entropy of the single centered black hole also represents the logarithm of the index carried by the same black hole.”