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67
Fusion in conformal field theory as the tensor product of the symmetry algebra
 Int. Journ. Mod. Phys. A9
, 1994
"... the symmetry algebra ..."
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 18 (9 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
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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Cited by 14 (2 self)
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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 14 (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....
On Conformal Field Theory and Stochastic Loewner Evolution
, 2004
"... We describe Stochastic Loewner Evolution on arbitrary Riemann surfaces with boundary using Conformal Field Theory methods. We propose in particular a CFT construction for a probability measure on (clouded) paths, and check it against known restriction properties. The probability measure can be thoug ..."
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Cited by 13 (3 self)
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We describe Stochastic Loewner Evolution on arbitrary Riemann surfaces with boundary using Conformal Field Theory methods. We propose in particular a CFT construction for a probability measure on (clouded) paths, and check it against known restriction properties. The probability measure can be thought of as a section of the determinant bundle over moduli spaces of Riemann surfaces. Loewner evolutions have a natural description in terms of random walk in the moduli space, and the stochastic diffusion equation translates to the Virasoro action of a certain weighttwo operator on a uniformised version of the determinant bundle.
Involutions On Moduli Spaces And Refinements Of The Verlinde Formula
, 1997
"... The moduli space M of semistable rank 2 bundles with trivial determinant over a complex curve \Sigma carries involutions naturally associated to 2torsion points on the Jacobian of the curve. For every lift of a 2torsion point to a 4torsion point, we define a lift of the involution to the determ ..."
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Cited by 12 (5 self)
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The moduli space M of semistable rank 2 bundles with trivial determinant over a complex curve \Sigma carries involutions naturally associated to 2torsion points on the Jacobian of the curve. For every lift of a 2torsion point to a 4torsion point, we define a lift of the involution to the determinant line bundle L. We obtain an explicit presentation of the group generated by these lifts in terms of the order 4 Weil pairing. This is related to the triple intersections of the components of the fixed point sets in M , which we also determine completely using the order 4 Weil pairing. The lifted involutions act on the spaces of holomorphic sections of powers of L, whose dimensions are given by the Verlinde formula. We compute the characters of these vector spaces as representations of the group generated by our lifts, and we obtain an explicit isomorphism (as group representations) with the combinatorialtopological TQFTvector spaces of [BHMV]. As an application, we describe a `brick...
Introduction to vertex algebras, Borcherds algebras, and the monster Lie algebra
 International Journal of Modern Physics
, 1993
"... ..."
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 11 (0 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.
On connections of conformal field theory and stochastic l?wner evolution
, 2004
"... This manuscript explores the connections between a class of stochastic processes called “Stochastic Loewner Evolution ” (SLE) and conformal field theory (CFT). First some important results are recalled which we utilise in the sequel, in particular the notion of conformal restriction and of the “rest ..."
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Cited by 8 (2 self)
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This manuscript explores the connections between a class of stochastic processes called “Stochastic Loewner Evolution ” (SLE) and conformal field theory (CFT). First some important results are recalled which we utilise in the sequel, in particular the notion of conformal restriction and of the “restrcition martingale”, originally introduced in [48]. Then an explicit construction of a link between SLE and the representation theory of the Virasoro algebra is given. In particular, we interpret the Ward identities in terms of the restriction property and the central charge in terms of the density of Brownian bubbles. We then show that this interpretation permits to relate the κ of the stochastic process with the central charge c of the conformal field theory. This is achieved by a highestweight representation which is degenerate at level two, of the Virasoro algebra. Then we proceed by giving a derivation of the same relations, but from the