scholarly journals Indefinite theta functions and black hole partition functions

2014 ◽  
Vol 2014 (2) ◽  
Author(s):  
Gabriel Lopes Cardoso ◽  
Michele Cirafici ◽  
Rogério Jorge ◽  
Suresh Nampuri
Keyword(s):  
Black Hole ◽  
Theta Functions ◽  
Partition Functions

scholarly journals Black hole hair removal for N = 4 CHL models

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Subhroneel Chakrabarti ◽  
Suresh Govindarajan ◽  
P. Shanmugapriya ◽  
Yogesh K. Srivastava ◽  
Amitabh Virmani
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Microscopic Analysis ◽  
Flat Space ◽  
Special Care ◽  
Hair Removal ◽  
Partition Functions ◽  
Rotating Black Holes

Abstract Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al. in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.

scholarly journals Generating functions and congruences for some partition functions related to mock theta functions

2019 ◽  
Vol 16 (02) ◽  
pp. 423-446 ◽  
Author(s):  
Nayandeep Deka Baruah ◽  
Nilufar Mana Begum
Keyword(s):  
Generating Functions ◽  
Theta Functions ◽  
Partition Functions ◽  
Mock Theta Functions ◽  
Third Order

Recently, Andrews, Dixit and Yee introduced partition functions associated with Ramanujan/Watson third-order mock theta functions [Formula: see text] and [Formula: see text]. In this paper, we find several new exact generating functions for those partition functions as well as the associated smallest part functions and deduce several new congruences modulo powers of 5.

scholarly journals Quantum black holes, elliptic genera and spectral partition functions

2014 ◽  
Vol 11 (05) ◽  
pp. 1450048 ◽  
Author(s):  
A. A. Bytsenko ◽  
M. Chaichian ◽  
R. J. Szabo ◽  
A. Tureanu
Keyword(s):  
Black Hole ◽  
Lie Algebras ◽  
Modular Forms ◽  
Partition Functions ◽  
Affine Lie Algebras ◽  
Hilbert Schemes ◽  
Spectral Functions ◽  
Infinite Dimensional ◽  
Elliptic Genera ◽  
Bps Invariants

We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic three-geometry associated with q-series in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local Calabi–Yau threefolds in terms of BPS invariants and spectral functions, and also of equivariant D-brane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.

scholarly journals Computing black hole partition functions from quasinormal modes

2016 ◽  
Vol 2016 (7) ◽  
Author(s):  
Peter Arnold ◽  
Phillip Szepietowski ◽  
Diana Vaman
Keyword(s):  
Black Hole ◽  
Quasinormal Modes ◽  
Partition Functions

UNCERTAINTY RELATION AND BLACK HOLE ENTROPY OF TOROIDAL SPACETIME

2004 ◽  
Vol 01 (06) ◽  
pp. 731-737
Author(s):  
SHUANG-QI HU ◽  
ZHAO REN
Keyword(s):  
Black Hole ◽  
Uncertainty Relation ◽  
Black Hole Entropy ◽  
State Density ◽  
Partition Functions ◽  
Brick Wall ◽  
Fermionic Field ◽  
Logarithmic Term ◽  
Horizon Topology ◽  
New Equation

By using the method of quantum statistics and via the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we avoid the difficulty of solving wave equation, and directly derive the partition functions of bosonic and fermionic field in Toroidal black hole. Then we calculate the entropies of bosonic and fermionic field near the black hole horizon on the background of a black hole. In our result, the divergent logarithmic term and ultraviolet cutoff in the original brick-wall method by which the black hole entropy was derived no longer exist. It is shown that the entropy of the black hole is proportional to the area of the horizon. These results are similar to that in the black hole with horizon topology S2.

STATISTICAL ENTROPY OF KERR BLACK HOLE

2002 ◽  
Vol 11 (09) ◽  
pp. 1381-1387 ◽  
Author(s):  
REN ZHAO ◽  
LICHUN ZHANG
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
State Density ◽  
Partition Functions ◽  
Brick Wall ◽  
Statistical Entropy ◽  
Fermionic Field ◽  
Logarithmic Term ◽  
Entropy Of Black Hole ◽  
Wall Method

Using the method of quantum statistics, we directly derive the partition functions of bosonic and fermionic field in Kerr black hole with axial symmetry. Then via the improved brick-wall method for membrane model, we show that the entropy of the bosonic and fermionic field in the black hole is proportional to the area of the horizon. In our result, the stripped term and the divergent logarithmic term no longer exist. Hence the problem that the state density is divergent around the horizon doesn't exist. We also give the influence of the spining degeneracy of particles on the entropy of black hole. We offer a new simple and direct way of calculating the entropy of different complicated black holes.

scholarly journals Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kevin Goldstein ◽  
Vishnu Jejjala ◽  
Yang Lei ◽  
Sam van Leuven ◽  
Wei Li
Keyword(s):  
Black Hole ◽  
Chemical Potential ◽  
Specific Region ◽  
Partition Functions ◽  
Potential Space ◽  
Leading Order ◽  
Yang Mills ◽  
Superconformal Index ◽  
Chemical Potentials ◽  
Entropy Functions

Abstract We compute the superconformal index of the $$ \mathcal{N} $$ N = 4 SU(N) Yang-Mills theory through a residue calculation. The method is similar in spirit to the Bethe Ansatz formalism, except that all poles are explicitly known, and we do not require specialization of any of the chemical potentials. Our expression for the index allows us to revisit the Cardy limit using modular properties of four-dimensional supersymmetric partition functions. We find that all residues contribute at leading order in the Cardy limit. In a specific region of flavour chemical potential space, close to the two unrefined points, in fact all residues contribute universally. These universal residues precisely agree with the entropy functions of the asymptotically AdS5 black hole and its “twin saddle” respectively. Finally, we discuss how our formula is suited to study the implications of four-dimensional modularity for the index beyond the Cardy limit.

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