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hepth/9412126 Lie group weight multiplicities from conformal field theory
, 1994
"... Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of WessZuminoWitten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relation ..."
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Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of WessZuminoWitten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new
Elliptic WessZuminoWitten Model from Elliptic ChernSimons Theory
 LETT. MATH. PHYS
, 1995
"... This letter continues the program [17][12][20][21] aimed at analysis of the scalar product of states in the ChernSimons theory. It treats the elliptic case with group SU2. The formal scalar product is expressed as a multiple finite dimensional integral which, if convergent for every state, provides ..."
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Cited by 6 (2 self)
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, provides the space of states with a Hilbert space structure. The convergence is checked for states with a single Wilson line where the integral expressions encode the BetheAnsatz solutions of the Lamé equation. In relation to the WessZuminoWitten conformal field theory, the scalar product renders
UvADARE (Digital Academic Repository) Yangian symmetry in conformal field theory Yangian symmetry in conformal field theory
"... Abstract We show that the SU(N), level1 WessZuminoWitten conformal field theory provides a natural realization of the Yangian Y(sl~) for N _> 3. We also construct a hamiltonian//2 which commutes with the Yangian generators and study its spectrum. Our results, which generalize work by Haldane ..."
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Abstract We show that the SU(N), level1 WessZuminoWitten conformal field theory provides a natural realization of the Yangian Y(sl~) for N _> 3. We also construct a hamiltonian//2 which commutes with the Yangian generators and study its spectrum. Our results, which generalize work
W symmetry in conformal field theory, Phys
 Rep
, 1993
"... We show that the SU(N), level1 WessZuminoWitten conformal field theory provides a natural realization of the Yangian Y (slN) for N ≥ 3. We also construct a hamiltonian H2 which commutes with the Yangian generators and study its spectrum. Our results, which generalize work by Haldane et al. [1], p ..."
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Cited by 44 (1 self)
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We show that the SU(N), level1 WessZuminoWitten conformal field theory provides a natural realization of the Yangian Y (slN) for N ≥ 3. We also construct a hamiltonian H2 which commutes with the Yangian generators and study its spectrum. Our results, which generalize work by Haldane et al. [1
Purely affine elementary su(N) fusions
, 2001
"... We consider threepoint couplings in simple Lie algebras – singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary couplings. This carries over to affine fusion, the fusion of W ..."
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of WessZuminoWitten conformal field theories, where the expressions are in terms of elementary fusions. In the case of su(4) it has been observed that there is a purely affine elementary fusion, i.e., an elementary fusion that is not an elementary coupling. In this note we show by construction
Affine and Yangian Symmetries in SU(2)1 Conformal Field Theory ∗
, 1994
"... In these lectures, we study and compare two different formulations of SU(2), level k = 1, WessZuminoWitten conformal field theory. The first, conventional, formulation employs the affine symmetry of the model; in this approach correlation functions are derived from the socalled KnizhnikZamolodch ..."
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Cited by 3 (1 self)
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In these lectures, we study and compare two different formulations of SU(2), level k = 1, WessZuminoWitten conformal field theory. The first, conventional, formulation employs the affine symmetry of the model; in this approach correlation functions are derived from the socalled Knizhnik
Spinon bases, Yangian symmetry and fermionic representations of Virasoro characters in conformal field theory, Phys
 Lett. B
, 1994
"... Abstract We study the description of the SU(2), level k = 1, WessZuminoWitten conformal field theory in terms of the modes of the spin1/2 affine primary field ff'~. These are shown to satisfy generalized 'canonical commutation relations', which we use to construct a basis of Hilbe ..."
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Cited by 21 (3 self)
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Abstract We study the description of the SU(2), level k = 1, WessZuminoWitten conformal field theory in terms of the modes of the spin1/2 affine primary field ff'~. These are shown to satisfy generalized 'canonical commutation relations', which we use to construct a basis
On fusion algebras and modular matrices
 Commun. Math. Phys
, 1999
"... Abstract: We consider the fusion algebras arising in e.g. WessZuminoWitten conformal field theories, affine KacMoody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix S, we find small sets of primary fields (equivalently, sets of high ..."
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Cited by 8 (3 self)
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Abstract: We consider the fusion algebras arising in e.g. WessZuminoWitten conformal field theories, affine KacMoody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix S, we find small sets of primary fields (equivalently, sets
Quantum geometry and quantum algorithms
 J. Phys. A: Math. Theor
"... Abstract. Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on the complete solution of ChernSimons topological q ..."
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Cited by 2 (2 self)
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quantum field theory and its connection to WessZuminoWitten conformal field theory. The colored Jones polynomial is expressed as the expectation value of the evolution of the qdeformed spinnetwork quantum automaton. A quantum circuit is constructed capable of simulating the automaton and hence
An efficient quantum algorithm for colored Jones polynomials
, 2006
"... We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. Our construction is based on SU(2) ChernSimons topological quantum field theory (and associated WessZuminoWitten conformal field the ..."
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Cited by 1 (0 self)
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We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. Our construction is based on SU(2) ChernSimons topological quantum field theory (and associated WessZuminoWitten conformal field
Results 1  10
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5,112