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DAMTP1998135 hepth/9810019 AXIOMATIC CONFORMAL FIELD THEORY
, 1998
"... A new rigorous approach to conformal field theory is presented. The basic objects are families of complexvalued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators a ..."
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A new rigorous approach to conformal field theory is presented. The basic objects are families of complexvalued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators
Axiomatic quantum field theory in curved spacetime
, 2008
"... The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globa ..."
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Cited by 687 (18 self)
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The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary
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 1443 (45 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
The large N limit of superconformal field theories and supergravity
, 1998
"... We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and ..."
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Cited by 5629 (20 self)
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We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory
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 365 (0 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
Antide Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
 Adv. Theor. Math. Phys
, 1998
"... The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum phenome ..."
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Cited by 1083 (3 self)
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
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 381 (12 self)
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dimensions governs the space of “conformal blocks ” of the sixdimensional (0, 2) conformal field theory. December
Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties
 J. Alg. Geom
, 1994
"... We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined by ..."
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Cited by 467 (20 self)
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an isomorphism between two conformal field theories corresponding to CalabiYau varieties from two families F(∆) and F( ∆ ∗). 1
Results 1  10
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