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Large N field theories, string theory and gravity
, 2001
"... We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evide ..."
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Cited by 1125 (42 self)
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We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and nonconformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
ChernSimons Gauge Theory as a String Theory
, 2003
"... Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional ChernSimons gaug ..."
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Cited by 518 (13 self)
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Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional ChernSimons gauge theory can arise as a string theory. The worldsheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the spacetime ChernSimons theory. A certain holomorphic analog of ChernSimons theory can also arise as a string theory.
Localization of gauge theory on a foursphere and supersymmetric Wilson loops,” arXiv:0712.2824 [hepth
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Mirror Manifolds and Topological Field Theory
 in Essays on Mirror Manifolds (ed. S.T. Yau), International Press, Hong Kong
, 1992
"... In N = 4 super YangMills theory on a fourmanifold M, one can specify a discrete magnetic flux valued in H2 (M,ZN). This flux is encoded in the AdS/CFT correspondence in terms of a fivedimensional topological field theory with ChernSimons action. A similar topological field theory in seven dimens ..."
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Cited by 364 (14 self)
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In N = 4 super YangMills theory on a fourmanifold M, one can specify a discrete magnetic flux valued in H2 (M,ZN). This flux is encoded in the AdS/CFT correspondence in terms of a fivedimensional topological field theory with ChernSimons action. A similar topological field theory in seven dimensions governs the space of “conformal blocks ” of the sixdimensional (0, 2) conformal field theory. December
Anti de Sitter space and holography
, 1998
"... Recently, it has been proposed by Maldacena that large N limits of certain conformal field theories in d dimensions can be described in terms of supergravity (and string theory) on the product of d+1dimensional AdS space with a compact manifold. Here we elaborate on this idea and propose a precise ..."
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Cited by 346 (7 self)
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Recently, it has been proposed by Maldacena that large N limits of certain conformal field theories in d dimensions can be described in terms of supergravity (and string theory) on the product of d+1dimensional AdS space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the KaluzaKlein modes of Type IIB supergravity on AdS5×S5 match with the chiral operators of N = 4 super YangMills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the N = 4 theory has a large N phase transition related to the thermodynamics of AdS black holes. February
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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Cited by 326 (1 self)
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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.
ElectricMagnetic duality and the geometric Langlands program
, 2006
"... The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t H ..."
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Cited by 290 (23 self)
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The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke
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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Cited by 282 (35 self)
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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.
Relativistic Spin Networks and Quantum Gravity
 J. Math Phys
, 1998
"... Abstract. Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) × SU(2). Relativistic quantum spins are related to the geometry of the 2dimensional faces of a 4simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geome ..."
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Cited by 153 (16 self)
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Abstract. Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) × SU(2). Relativistic quantum spins are related to the geometry of the 2dimensional faces of a 4simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geometry of the edges of a 3simplex. This leads us to suggest that there may be a 4dimensional state sum model for quantum gravity based on relativistic spin networks which parallels the construction of 3dimensional quantum gravity from ordinary spin networks.
Topological Gauge Theories and Group Cohomology
, 1989
"... We show that three dimensional ChernSimons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H 4 (BG, Z). In a similar way, possible WessZumino interactions of such a group G are classified by H 3 (G, Z). ..."
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Cited by 153 (2 self)
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We show that three dimensional ChernSimons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H 4 (BG, Z). In a similar way, possible WessZumino interactions of such a group G are classified by H 3 (G, Z). The relation between three dimensional ChernSimons gauge theory and two dimensional sigma models involves a certain natural map from H 4 (BG, Z) to H 3 (G, Z). We generalize this correspondence to topological ‘spin ’ theories, which are defined on three manifolds with spin structure, and are related to what might be called Z2 graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.