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31
LECTURES ON CONFORMAL FIELD THEORY AND KACMOODY ALGEBRAS
, 1997
"... This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of KacMoody algebras. These lectures were held at the Graduate Course on Conformal Field Theory and Integrable Models (Budapest, August 1996). They will appear in a vo ..."
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Cited by 16 (1 self)
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This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of KacMoody algebras. These lectures were held at the Graduate Course on Conformal Field Theory and Integrable Models (Budapest, August 1996). They will appear in a volume of the Springer Lecture Notes in Physics edited by Z. Horvath and L. Palla.
SU(3)Goodmande la HarpeJones subfactors and the realisation of SU(3) modular invariants
, 2009
"... We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)modular invariant partition functions previously classified by Gannon. ..."
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Cited by 15 (9 self)
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We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)modular invariant partition functions previously classified by Gannon.
The classification of SU(3) modular invariants revisited
"... The SU(3) modular invariant partition functions were first completely classified in Ref. [9]. The purpose of these notes is fourfold: (i) Here we accomplish the SU(3) classification using only the most basic facts: modular invariance; Mλµ ∈ Z≥; and M00 = 1. In [9] we made use of less elementary res ..."
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Cited by 12 (4 self)
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The SU(3) modular invariant partition functions were first completely classified in Ref. [9]. The purpose of these notes is fourfold: (i) Here we accomplish the SU(3) classification using only the most basic facts: modular invariance; Mλµ ∈ Z≥; and M00 = 1. In [9] we made use of less elementary results from MooreSeiberg, in addition to these 3 basic facts. (ii) Ref. [9] was completed well over a year ago. Since then I have found a number of significant simplifications to the general argument. They are all included here. (iii) A number of people have complained that some of the arguments in [9] were hard to follow. I have tried here to be as explicit and as clear as possible. (iv) Hidden in [9] were a number of smaller results which should be of independent value. These are explicitly mentioned here. This paper focuses exclusively on the classification of SU(3) WZNW partition functions, though many of the results and techniques work in much greater generality. See [9] for the motivation for the problem.
Ocneanu cells and Boltzmann weights for the SU(3) . . .
, 2009
"... We determine the cells, whose existence has been announced by Ocneanu, on all the candidate nimrep graphs except E (12) 4 proposed by di Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This enables the Boltzmann weights to be computed for the corresponding integrable stati ..."
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Cited by 11 (8 self)
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We determine the cells, whose existence has been announced by Ocneanu, on all the candidate nimrep graphs except E (12) 4 proposed by di Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This enables the Boltzmann weights to be computed for the corresponding integrable statistical mechanical models and provide the framework for studying corresponding braided subfactors to realise all the SU(3) modular invariants as well as a framework for a new SU(3) planar algebra theory.
On Algebraic Singularities, Finite Graphs and DBrane Gauge Theories: A String Theoretic Perspective
, 2002
"... In this writing we shall address certain beautiful interrelations between the construction of 4dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such ..."
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Cited by 11 (8 self)
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In this writing we shall address certain beautiful interrelations between the construction of 4dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such as orbifolds, symplectic quotients and quiver representations, as well as the physics, such as gauged linear sigma models, geometrical engineering, HananyWitten setups and Dbrane probes. We investigate aspects of worldvolume gauge dynamics using Dbrane resolutions of various CalabiYau singularities, notably Gorenstein quotients and toric singularities. Attention will be paid to the general methodology of constructing gauge theories for these singular backgrounds, with and without the presence of the NSNS Bfield, as well as the Tduals to brane setups and branes wrapping cycles in the mirror geometry. Applications of such diverse and elegant mathematics as crepant resolution of algebraic singularities, representation of finite groups and finite graphs, modular invariants of affine Lie algebras, etc. will naturally arise. Various viewpoints and generalisations of McKay’s Correspondence will also be considered. The present work is a transcription of excerpts from the first three volumes of the author’s PhD thesis which was written under the direction of Prof. A. Hanany to whom he is much indebted at the Centre for Theoretical Physics of MIT, and which, at the suggestion of friends, he posts to the ArXiv pro hac vice; it is his sincerest wish that the ensuing pages might be of some small use to the beginning student.
Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory
, 2009
"... We determine spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with SU(3) modular invariants and subgroups of SU(3). Our methods also give an alternative approach to deriving the results of Banica and Bisch for ADE graphs and subgroups of SU(2) and e ..."
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Cited by 10 (9 self)
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We determine spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with SU(3) modular invariants and subgroups of SU(3). Our methods also give an alternative approach to deriving the results of Banica and Bisch for ADE graphs and subgroups of SU(2) and explain the connection between their results for affine ADE graphs and the Kostant polynomials. We also look at the Hilbert generating series of associated preprojective algebras.
Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus
 J MATH PHYS 48 P 043511
, 2006
"... After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and cosemisimple blocks of the corresponding weak bialgebras (quantum ..."
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Cited by 10 (5 self)
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After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and cosemisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction restriction. For reasons of size, the sl(3) tables of induction are only given for theories with selffusion (existence of a monoidal structure).
A2planar algebras II: Planar modules
, 2009
"... Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2planar algebra capturing the structure contained in the SU(3) ADE subfactors. We now introduce the notion of modules over an A2planar algebra, and describe certain irreducible Hilbert A2TLmodules. A partial decom ..."
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Cited by 6 (6 self)
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Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2planar algebra capturing the structure contained in the SU(3) ADE subfactors. We now introduce the notion of modules over an A2planar algebra, and describe certain irreducible Hilbert A2TLmodules. A partial decomposition of the A2planar algebras for the ADE nimrep graphs associated to SU(3) modular invariants is achieved.
Comments about quantum symmetries of SU(3) graphs
, 2006
"... For the SU(3) system of graphs generalizing the ADE Dynkin digrams in the classification of modular invariant partition functions in CFT, we present a general collection of algebraic objects and relations that describe fusion properties and quantum symmetries associated with the corresponding Ocnean ..."
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Cited by 5 (4 self)
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For the SU(3) system of graphs generalizing the ADE Dynkin digrams in the classification of modular invariant partition functions in CFT, we present a general collection of algebraic objects and relations that describe fusion properties and quantum symmetries associated with the corresponding Ocneanu quantum groupoïds. We also summarize the properties of the individual members of this system.