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5,632
On conformal field theories
 in fourdimensions,” Nucl. Phys. B533
, 1998
"... We review the generalization of field theory to spacetime with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last ..."
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We review the generalization of field theory to spacetime with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. Submitted to Reviews of Modern Physics.
Black Hole Entropy Function, Attractors and Precision Counting of Microstates
, 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 ..."
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Cited by 324 (28 self)
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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 multicentered black holes as well.
Renormalization group flows from holography  Supersymmetry and a ctheorem
 ADV THEOR. MATH. PHYS
, 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. ..."
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Cited by 294 (25 self)
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We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N = 4 superYangMills theory broken to an N = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior antide Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N = 4 gauged supergravity theory holographically dual to a sector of N = 2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a cfunction that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For evendimensional boundaries, the cfunction coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.
Bethe Ansatz for Quantum Strings
, 2004
"... We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed allloop gauge theory asymptotic Bethe ansatz by add ..."
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Cited by 281 (16 self)
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We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed allloop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of Mimpurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M = 2, 3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 4 √ n 2 λ asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our
On the gauge theory/geometry correspondence
 Adv. Theor. Math. Phys
, 1999
"... The ’t Hooft expansion of SU(N) ChernSimons theory on S3 is proposed to be exactly dual to the topological closed string theory on the S2 blow up of the conifold geometry. The Bfield on the S2 has magnitude Ngs = λ, the ’t Hooft coupling. We are able to make a number of checks, such as finding exa ..."
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The ’t Hooft expansion of SU(N) ChernSimons theory on S3 is proposed to be exactly dual to the topological closed string theory on the S2 blow up of the conifold geometry. The Bfield on the S2 has magnitude Ngs = λ, the ’t Hooft coupling. We are able to make a number of checks, such as finding exact agreement at the level of the partition function computed on both sides for arbitrary λ and to all orders in 1/N. Moreover, it seems possible to derive this correspondence from a linear sigma model description of the conifold. We propose a picture whereby a perturbative Dbrane description, in terms of holes in the closed string worldsheet, arises automatically from the coexistence of two phases in the underlying U(1) gauge theory. This approach holds promise for a derivation of the AdS/CFT correspondence.
Breaking an Abelian gauge symmetry near a black hole horizon
, 2008
"... I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct. ..."
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I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.
Superstrings and topological strings at large
 N”, J. Math. Phys
"... We embed the large N ChernSimons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N = 1 supersymmetry in 4 dimensions and superstrings propagating on noncompact CalabiYau manifolds with certain fluxes turned on. We a ..."
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Cited by 254 (27 self)
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We embed the large N ChernSimons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N = 1 supersymmetry in 4 dimensions and superstrings propagating on noncompact CalabiYau manifolds with certain fluxes turned on. We also show that in a particular limit of the N = 1 gauge theory system, certain superpotential terms in the N = 1 system (including deformations if spacetime is noncommutative) are captured to all orders in 1/N by the amplitudes of noncritical bosonic strings propagating on a circle with selfdual radius. We also consider Dbrane/antiDbrane system wrapped over vanishing cycles of compact CalabiYau manifolds and argue that at large N they induce a shift in the background to a topologically distinct CalabiYau, which we identify as the ground state system of the Brane/antiBrane system. August
The factorized Smatrix of CFT/AdS
, 2004
"... We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s dilatati ..."
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We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s dilatation operator nor the string sigma model’s quantum Hamiltonian, but instead the respective factorized Smatrix. To illustrate the idea, we focus on the closed fermionic su(11) sector of the N = 4 gauge theory. We introduce a new technique, the perturbative asymptotic Bethe ansatz, and use it to extract this sector’s threeloop Smatrix from Beisert’s involved algebraic work on the threeloop su(23) sector. We then show that the current knowledge about semiclassical and nearplanewave quantum strings in the su(2), su(11) and sl(2) sectors of AdS5 ×S 5 is fully consistent with the existence of a factorized Smatrix. Analyzing the available information, we find an intriguing relation between the three associated Smatrices. Assuming that the relation also holds in gauge theory, we derive the threeloop Smatrix of the sl(2) sector even though this sector’s dilatation operator is not yet known beyond one loop. The resulting