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92
Fusion in conformal field theory as the tensor product of the symmetry algebra
 Int. Journ. Mod. Phys. A9
, 1994
"... the symmetry algebra ..."
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The Bekenstein bound, topological quantum field theory and pluralistic quantum cosmology
, 2008
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Representations of the homotopy surface category of a simply connected space
 J. Knot Theory and Ramifications
"... At the heart of the axiomatic formulation of 1+1dimensional topological field theory is the set of all surfaces with boundary assembled into a category. This category of surfaces has compact 1manifolds as objects and smooth oriented cobordisms as morphisms. Taking disjoint unions gives a monoidal ..."
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Cited by 22 (11 self)
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At the heart of the axiomatic formulation of 1+1dimensional topological field theory is the set of all surfaces with boundary assembled into a category. This category of surfaces has compact 1manifolds as objects and smooth oriented cobordisms as morphisms. Taking disjoint unions gives a monoidal
Modular functors are determined by their genus zero data
, 2006
"... We prove in this paper that the genus zero data of a modular functor determines the modular functor. We do this by establishing that the Smatrix in genus one with one point labeled arbitrarily can be expressed in terms of the genus zero information and we give an explicit formula. We do not assum ..."
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Cited by 20 (9 self)
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We prove in this paper that the genus zero data of a modular functor determines the modular functor. We do this by establishing that the Smatrix in genus one with one point labeled arbitrarily can be expressed in terms of the genus zero information and we give an explicit formula. We do not assume the modular functor in question has duality or is unitary, in order to establish this.
Global aspects of gauged WessZuminoWitten models
 Commun. Math. Phys
, 1996
"... A study of the gauged WessZuminoWitten models is given focusing on the effect of topologically nontrivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasiparabolic structure. Two actions of the fundamental gr ..."
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A study of the gauged WessZuminoWitten models is given focusing on the effect of topologically nontrivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasiparabolic structure. Two actions of the fundamental group of the gauge group is defined: One on the space of gauge invariant local fields and the other on the moduli spaces. Applying these in the integral expression, we obtain a certain identity which relates correlation functions for configurations of different topologies. It gives an important information on the topological sum for the partition and correlation functions. 1.
Quantum Deformation of Quantum Gravity
, 1996
"... We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum gravity characterized by states which are normalizable in the meas ..."
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Cited by 20 (2 self)
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We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum gravity characterized by states which are normalizable in the measure of ChernSimons theory. The deformation parameter, q, is e i¯h 2 G 2 =6 , where is the cosmological constant. The Mandelstam identities are extended to a set of relations which are governed by the Kauffman bracket so that the spin network basis is deformed to a basis of SU(2) q spin networks. Corrections to the actions of operators in nonperturbative quantum gravity may be readily computed using recoupling theory; the example of the area observable is treated here. Finally, eigenstates of the qdeformed Wilson loops are constructed, which may make possible the construction of a qdeformed connection representation through an inverse transform. internet addresses: seth@phys.psu....
Lectures on mirror symmetry, derived categories and Dbranes, Uspehi Mat
 arXiv:math.AG/0308173]; Remarks on Abranes, mirror symmetry, and the Fukaya
, 2003
"... Abstract. This is an introduction to Homological Mirror Symmetry, derived categories, and topological Dbranes aimed at a mathematical audience. In the last lecture we explain why it is necessary to enlarge the Fukaya category with coisotropic Abranes and discuss how to extend the definition of Flo ..."
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Cited by 19 (1 self)
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Abstract. This is an introduction to Homological Mirror Symmetry, derived categories, and topological Dbranes aimed at a mathematical audience. In the last lecture we explain why it is necessary to enlarge the Fukaya category with coisotropic Abranes and discuss how to extend the definition of Floer homology to such objects. These lectures were delivered at IPAM, March 2003, as part of a program on Symplectic Geometry and Physics. 1. Mirror Symmetry From a Physical Viewpoint The goal of this lecture is to explain the physicists ’ viewpoint of the Mirror Phenomenon and its interpretation in mathematical terms proposed by Maxim Kontsevich in his 1994 talk at the International Congress of Mathematicians [1]. Another approach to Mirror Symmetry was proposed by A. Strominger, ST. Yau, and E. Zaslow [2], but we will not discuss it here. From the physical point of view, Mirror Symmetry is a relation between 2d conformal field theories with N = 2 supersymmetry. A 2d conformal field theory is a rather complicated algebraic object whose definition will be sketched in a moment. Thus Mirror Symmetry originates in the realm of algebra/analysis. Geometry will appear later, when we specialize to a particular class of N = 2 superconformal field theories related to CalabiYau manifolds.
The WittenReshetikhinTuraev invariants of finite order mapping tori II
"... ar ..."
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Conformal Field Theory in Four and Six Dimensions”, arXiv:0712.0157
 Special Reduced Multiplets and Minimal Representations for Sp(n,R) 14 Λ−0 ❄ Λ−a ❄ • Λ+a ❄ Λ+0
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