Results 1  10
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907
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 383 (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
Virtual Knot Theory
 European J. Comb
, 1999
"... This paper is an introduction to the theory of virtual knots. It is dedicated to the memory of Francois Jaeger. 1 ..."
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Cited by 341 (39 self)
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This paper is an introduction to the theory of virtual knots. It is dedicated to the memory of Francois Jaeger. 1
Feynman diagrams and lowdimensional topology
, 2006
"... We shall describe a program here relating Feynman diagrams, topology of manifolds, homotopical algebra, noncommutative geometry and several kinds of “topological physics”. The text below consists of 3 parts. The first two parts (topological sigma model and ChernSimons theory) are formally independ ..."
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Cited by 224 (3 self)
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We shall describe a program here relating Feynman diagrams, topology of manifolds, homotopical algebra, noncommutative geometry and several kinds of “topological physics”. The text below consists of 3 parts. The first two parts (topological sigma model and ChernSimons theory) are formally independent and could be read separately. The third part describes the common algebraic background of both theories.
Chern–Simons Perturbation Theory
 II,” J. Diff. Geom
, 1994
"... Abstract. We study the perturbation theory for three dimensional Chern–Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the Lorentz gauge has a superspace formulation. The bas ..."
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Cited by 164 (2 self)
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Abstract. We study the perturbation theory for three dimensional Chern–Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the Lorentz gauge has a superspace formulation. The basic properties of the propagator and the Feynman rules are written in a precise manner in the language of differential forms. Using the explicit description of the propagator singularities, we prove that the theory is finite. Finally the anomalous metric dependence of the 2loop partition function on the Riemannian metric (which was introduced to define the gauge fixing) can be cancelled by a local counterterm as in the 1loop case [28]. In fact, the counterterm is equal to the Chern–Simons action of the metric connection, normalized precisely as one would expect based on the framing dependence of Witten’s exact solution.
Quantum Field Theory of ManyBody Systems
, 2004
"... condensation Extended objects, such as strings and membranes, have been studied for many years in the context of statistical physics. In these systems, quantum effects are typically negligible, and the extended objects can be treated classically. Yet it is natural to wonder how strings and membrane ..."
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Cited by 155 (4 self)
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condensation Extended objects, such as strings and membranes, have been studied for many years in the context of statistical physics. In these systems, quantum effects are typically negligible, and the extended objects can be treated classically. Yet it is natural to wonder how strings and membranes behave in the quantum regime. In this chapter, we will investigate the properties of one dimensional, stringlike, objects with large quantum fluctuations. Our motivation is both intellectual curiosity and (as we will see) the connection between quantum strings and topological/quantum orders in condensed matter systems. It is useful to organize our discussion using the analogy to the well understood theory of quantum particles. One of the most remarkable phenomena in quantum manyparticle systems is particle condensation. We can think of particle condensed states as special ground states where all the particles are described by the same quantum wave function. In some sense, all the symmetry breaking phases examples of particle condensation: we can view the order parameter that characterizes a symmetry breaking phase as the condensed wave function of certain “effective particles. ” According to this point of view, Landau’s theory [Landau (1937)] for symmetry breaking phases is really a theory of “particle ” condensation. The theory of particle condensation is based on the physical concepts of long range order, symmetry
Conformal blocks and generalized theta functions
 Comm. Math. Phys
, 1994
"... The aim of this paper is to construct a canonical isomorphism between two vector spaces associated to a Riemann surface X. The first of these spaces is the space of conformal blocks Bc(r) (also called the space of vacua), which plays an important role in conformal field theory. It is defined as foll ..."
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Cited by 141 (8 self)
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The aim of this paper is to construct a canonical isomorphism between two vector spaces associated to a Riemann surface X. The first of these spaces is the space of conformal blocks Bc(r) (also called the space of vacua), which plays an important role in conformal field theory. It is defined as follows: choose a point p ∈ X, and let AX be the
Lectures on 2D YangMills Theory, Equivariant Cohomology and Topological Field Theories
, 1996
"... These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying ..."
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Cited by 139 (13 self)
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These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.
Quantum gravity in 2 + 1 dimensions . . .
 LIVING REVIEWS IN RELATIVITY
, 2005
"... In three spacetime dimensions, general relativity drastically simplifies, becoming a “topological” theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body o ..."
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Cited by 137 (0 self)
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In three spacetime dimensions, general relativity drastically simplifies, becoming a “topological” theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)dimensional vacuum gravity in the setting of a spatially closed universe.
Matrix Model as a Mirror of ChernSimons Theory
, 2002
"... Using mirror symmetry, we show that ChernSimons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of ChernSimons theory. ..."
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Cited by 131 (24 self)
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Using mirror symmetry, we show that ChernSimons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of ChernSimons theory. Moreover, large N dualities in this context lead to computation of all genus Amodel topological amplitudes on toric CalabiYau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these CalabiYau manifolds with wrapped D6 branes (which are dual to Mtheory on G2 manifolds) this leads to engineering and solving Fterms for N = 1 supersymmetric gauge theories with superpotentials involving certain multitrace operators