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Split states, entropy enigmas, holes and halos (0)

by F Denef, G W Moore
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Black Hole Entropy Function, Attractors and Precision Counting of Microstates

by Ashoke Sen , 2007
"... In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric strin ..."
Abstract - Cited by 324 (28 self) - Add to MetaCart
In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric string theories, and compare the statistical entropy of these dyons, expanded in inverse powers of electric and magnetic charges, with a similar expansion of the corresponding black hole entropy. This comparison is extended to include the contribution to the entropy from multi-centered black holes as well.
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...Finally in §5.7 we demonstrate how the change in the degeneracy across walls of marginal stability can be related to (dis)appearance of 2-centered black holes as we cross the marginal stability walls =-=[136,137,138,139,140,141,142,143]-=-. Throughout this section we shall set α ′ = 1 unless mentioned otherwise. Our counting of states will follow [6,7,8]. The original formula for the degeneracy was first proposed in [9] for the special...

Curve counting via stable pairs in the derived category

by R. Pandharipande, R. P. Thomas , 2009
"... For a nonsingular projective 3-fold X, we define integer invariants virtually enumerating pairs (C,D) where C ⊂ X is an embedded curve and D ⊂ C is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of X. The resulting in ..."
Abstract - Cited by 114 (21 self) - Add to MetaCart
For a nonsingular projective 3-fold X, we define integer invariants virtually enumerating pairs (C,D) where C ⊂ X is an embedded curve and D ⊂ C is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of X. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of X. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category. Several calculations of the new invariants are carried out. In the Fano case, the local contributions of nonsingular embedded curves are found. In the local toric Calabi-Yau case, a completely new form of the topological vertex is described. The virtual enumeration of pairs is closely related to the geometry underlying the BPS state counts of Gopakumar and Vafa. We
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...o the derived category and made to include the virtual class, our entire discussion here remains conjectural. Similar phenomena have been observed recently in a noncommutative example [49]. The paper =-=[13]-=- also studies counting invariants (and more generally BPS states) and wall crossing in D b (X) from a physical point of view. In fact, Denef and Moore predict a wall crossing of precisely the form (3....

Non-commutative Donaldson-Thomas theory and the conifold

by Balázs Szendrői , 2008
"... Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson–Thomas invariants of Calabi–Yau threefolds. For the special case when A is the non-commutative crepant resolution of the th ..."
Abstract - Cited by 63 (0 self) - Add to MetaCart
Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson–Thomas invariants of Calabi–Yau threefolds. For the special case when A is the non-commutative crepant resolution of the threefold ordinary double point, it is proved using torus localization that the invariants count certain pyramid-shaped partition-like configurations, or equivalently infinite dimer configurations in the square dimer model with a fixed boundary condition. The resulting partition function admits an infinite product expansion, which factorizes into the rank-1 Donaldson–Thomas partition functions of the commutative crepant resolution of the singularity and its flop. The different partition functions are speculatively interpreted as counting stable objects in the derived category of A-modules under different stability conditions; their relationship should then be an instance of wall crossing in the space of stability conditions on this triangulated category.

Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1

by Tatsuo Azeyanagi, Tatsuma Nishioka, Tadashi Takayanagi , 2007
"... We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and derive this claim from AdS3/CFT2. We also analytically compute the entangl ..."
Abstract - Cited by 48 (8 self) - Add to MetaCart
We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and derive this claim from AdS3/CFT2. We also analytically compute the entanglement entropy in the two dimensional CFT of a free Dirac fermion compactified on a circle at finite temperature. From this result, we clarify the relation between the thermal entropy and entanglement entropy, which is essential for the entanglement interpretation of black hole entropy.

Wall crossing in local Calabi Yau manifolds

by Daniel L. Jafferis, Gregory W. Moore , 2008
"... We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kähler parameter of the rigid P 1 it is necessary to introduce an extra real parameter to describe BPS partition functions and marginal stability wa ..."
Abstract - Cited by 46 (3 self) - Add to MetaCart
We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kähler parameter of the rigid P 1 it is necessary to introduce an extra real parameter to describe BPS partition functions and marginal stability walls. The supergravity approach to BPS statecounting gives a simple derivation of results of Szendrői concerning Donaldson-Thomas theory on the noncommutative conifold. This example also illustrates some interesting limitations on the supergravity approach to BPS state-counting and wall-crossing.

Wall-crossing from supersymmetric galaxies,” arXiv:1008.0030 [hep-th

by Evgeny Andriyash, Frederik Denef, Daniel L. Jafferis, Gregory W. Moore
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Abstract - Cited by 35 (6 self) - Add to MetaCart
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...elman proposed a remarkable wall crossing formula for BPS indices. In this note we show that this formula can be derived in an elementary way from the halo picture of BPS bound states in supergravity =-=[4, 5]-=-. The basic strategy we follow is similar to that of [9], which gave a proof of the (motivic) KS wall-crossing formula in the context of N = 2 field theory. The essential physical idea used halo confi...

Quantum Entropy Function from AdS(2)/CFT(1) Correspondence

by Ashoke Sen , 2008
"... We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of ..."
Abstract - Cited by 34 (9 self) - Add to MetaCart
We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry, – named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical
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...ieved for a class of black holes in N = 4 supersymmetric string theories [2,3,4,5]. Significant progress has also been made for half BPS black holes in a class of N = 2 supersymmetric string theories =-=[6,7,8]-=-. The other front involves understanding how higher derivative corrections / string loop corrections affect the black hole entropy. Wald’s formalism [9,10,11,12] gives a clear prescription for calcula...

Supersymmetric gauge theories, intersecting branes and free fermions

by Robbert Dijkgraaf, Lotte Hollands, Piotr Sułkowski , Cumrun Vafa , 2007
"... ..."
Abstract - Cited by 33 (6 self) - Add to MetaCart
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Two centered black holes and N=4 dyon spectrum

by Ashoke Sen
"... The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy ..."
Abstract - Cited by 30 (16 self) - Add to MetaCart
The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy
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...rwise the condition on Q · P stated in the proposal will be reversed. With the sign convention for d( ⃗ Q, ⃗ P) described in footnote 2 this assumption is consistent with the wall crossing formula of =-=[18,33]-=-. 63 Two Centered Small Black Holes For describing the two centered black hole we shall use the N = 2 supersymmetric description of the same system described above. In the supergravity approximation ...

Quantum Geometry of Refined Topological Strings

by Mina Aganagic, Miranda C. N. Cheng, Robbert Dijkgraaf, Daniel Krefl, Cumrun Vafa , 2011
"... ..."
Abstract - Cited by 30 (6 self) - Add to MetaCart
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