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Twisted KTheory and KTheory of Bundle Gerbes
 COMMUN. MATH. PHYS
, 2002
"... In this note we introduce the notion of bundle gerbe Ktheory and investigate the relation to twisted Ktheory. We provide some examples. Possible applications of bundle gerbe Ktheory to the classification of Dbrane charges in nontrivial backgrounds are briefly discussed. ..."
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Cited by 140 (32 self)
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In this note we introduce the notion of bundle gerbe Ktheory and investigate the relation to twisted Ktheory. We provide some examples. Possible applications of bundle gerbe Ktheory to the classification of Dbrane charges in nontrivial backgrounds are briefly discussed.
Hole Entropy From Conformal Field Theory
 In Any Dimension” , hepth/9812013
"... When restricted to the horizon of a black hole, the “gauge ” algebra of surface deformations in general relativity contains a physically important Virasoro subalgebra with a calculable central charge. The fields in any quantum theory of gravity must transform under this algebra; that is, they must a ..."
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Cited by 98 (1 self)
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When restricted to the horizon of a black hole, the “gauge ” algebra of surface deformations in general relativity contains a physically important Virasoro subalgebra with a calculable central charge. The fields in any quantum theory of gravity must transform under this algebra; that is, they must admit a conformal field theory description. With the aid of Cardy’s formula for the asymptotic density of states in a conformal field theory, I use this description to derive the BekensteinHawking entropy. This method is universal—it holds for any black hole, in any dimension, and requires no details of quantum gravity—but it is also explicitly statistical mechanical, based on the counting of microscopic states.
Low energy hadron physics in holographic QCD”, Prog. Theor. Phys
 113 (2005) 843, hepth/0412141; “More on a holographic dual of QCD”, Prog. Theor. Phys. 114 (2006) 1083, hepth/0507073
"... We present a holographic dual of fourdimensional, large Nc QCD with massless flavors. This model is constructed by placing Nf probe D8branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8D8 pairs in ..."
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Cited by 98 (1 self)
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We present a holographic dual of fourdimensional, large Nc QCD with massless flavors. This model is constructed by placing Nf probe D8branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8D8 pairs in the supergravity background. The meson spectrum is examined by analyzing a fivedimensional YangMills theory that originates from the nonAbelian DBI action of the probe D8brane. It is found that our model yields massless pions, which are identified with NambuGoldstone bosons associated with the chiral symmetry breaking. We obtain the lowenergy effective action of the pion field and show that it contains the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon is identified with the Skyrmion. We also derive the effective action including the lightest vector meson. Our model is closely related to that in the hidden local symmetry approach, and we obtain a KawarabayashiSuzukiRiazuddinFayyazuddintype relation among the couplings. Furthermore, we investigate the ChernSimons term on the probe brane and show that it leads to the WessZuminoWitten term. The mass of the η ′ meson is also considered, and we formulate a simple derivation of the η ′ mass term satisfying the WittenVeneziano formula from supergravity.
Threedimensional gauge dynamics from brane configurations with (p,q)fivebrane,” Nucl
 Phys. B 539
, 1999
"... We study threedimensional gauge dynamics by using type IIB superstring brane configurations, which can be obtained from the Mtheory configuration of M2branes stretched between two M5branes with relative angles. Our construction of brane configurations includes (p, q)5brane and gives a systemati ..."
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Cited by 85 (4 self)
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We study threedimensional gauge dynamics by using type IIB superstring brane configurations, which can be obtained from the Mtheory configuration of M2branes stretched between two M5branes with relative angles. Our construction of brane configurations includes (p, q)5brane and gives a systematic classification of possible threedimensional gauge theories. The explicit identification of gauge theories are made and their mirror symmetry is discussed. As a new feature, our theories include interesting MaxwellChernSimons system whose vacuum structure is also examined in detail, obtaining results consistent with the brane picture.
Threedimensional quantum geometry and black holes
"... We review some aspects of threedimensional quantum gravity with emphasis in the ‘CFT → Geometry ’ map that follows from the BrownHenneaux conformal algebra. The general solution to the classical equations of motion with antide Sitter boundary conditions is displayed. This solution is parametrized ..."
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Cited by 76 (3 self)
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We review some aspects of threedimensional quantum gravity with emphasis in the ‘CFT → Geometry ’ map that follows from the BrownHenneaux conformal algebra. The general solution to the classical equations of motion with antide Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantisation. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the BekensteinHawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in 2+1 gravity is analysed in detail using a Hamiltonian ChernSimons formalism. 1
Twisted Ktheory of differentiable stacks
 ANN. SCI. ÉCOLE NORM. SUP
, 2004
"... In this paper, we develop twisted Ktheory for stacks, where the twisted class is given by an S 1gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K i α ⊗K j β → Ki+j α+β are derived. Our approach provides a uniform framew ..."
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Cited by 75 (13 self)
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In this paper, we develop twisted Ktheory for stacks, where the twisted class is given by an S 1gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K i α ⊗K j β → Ki+j α+β are derived. Our approach provides a uniform framework for studying various twisted Ktheories including the usual twisted Ktheory of topological spaces, twisted equivariant Ktheory, and the twisted Ktheory of orbifolds. We also present a Fredholm picture, and discuss the conditions under which twisted Kgroups can be expressed by socalled “twisted vector bundles”. Our approach is to work on presentations of stacks, namely groupoids, and relies heavily on the machinery of Ktheory (KKtheory) of C ∗algebras.
Entropy from Conformal Field Theory at Killing Horizons
, 1999
"... On a manifold with boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of boundary conditions leads to a Virasoro subalgebra with a calculab ..."
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Cited by 70 (2 self)
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On a manifold with boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of boundary conditions leads to a Virasoro subalgebra with a calculable central charge. Conformal field theory methods may then be used to determine the density of states at the boundary. I consider a number of cases—black holes, Rindler space, de Sitter space, TaubNUT and TaubBolt spaces, and dilaton gravity—and show that the resulting density of states yields the expected BekensteinHawking entropy. The statistical mechanics of black hole entropy may thus be fixed by symmetry arguments, independent of details of quantum gravity.
What we don’t know about BTZ black hole entropy
, 1998
"... With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the “statistical mechanics ” of the (2+1)dimensional black hole of Bañados, Teitelboim, and Zanelli (BTZ) ..."
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Cited by 62 (2 self)
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With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the “statistical mechanics ” of the (2+1)dimensional black hole of Bañados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations of the BTZ entropy exist, but none is completely satisfactory, and many questions remain open: there is no consensus as to what fields provide the relevant degrees of freedom or where these excitations live. In this paper, I review some of the unresolved problems and suggest avenues for their solution.
Dbranes on CalabiYau manifolds
, 2004
"... In this review we study BPS Dbranes on Calabi–Yau threefolds. Such Dbranes naturally divide into two sets called Abranes and Bbranes which are most easily understood from topological field theory. The main aim of this paper is to provide a selfcontained guide to the derived category approach to ..."
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Cited by 58 (8 self)
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In this review we study BPS Dbranes on Calabi–Yau threefolds. Such Dbranes naturally divide into two sets called Abranes and Bbranes which are most easily understood from topological field theory. The main aim of this paper is to provide a selfcontained guide to the derived category approach to Bbranes and the idea of Πstability. We argue that this mathematical machinery is hard to avoid for a proper understanding of Bbranes. Abranes and Bbranes are related in a very complicated and interesting way which ties in with the “homological mirror symmetry ” conjecture of Kontsevich. We motivate and exploit this form of mirror symmetry. The examples of the quintic 3fold, flops and orbifolds are discussed at some length. In the latter