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KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K

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DAVID OLIVE

Blackett Laboratory, Imperial College, London SW7 2BZ, U.K

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https://doi.org/10.1142/S0217751X86000149Cited by:763 (Source: Crossref)

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- Geometry of conformal mechanics
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- Spontaneous symmetry breaking of affine field theory
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- Representation of the so(N) and u(N) superconformal algebras via Miura transformations
  Pierre Mathieu
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- Trigonometric structure constants for new infinite-dimensional algebras
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- Quantum equivalence of coset space models
  Daniel Altschuler
  1 Feb 1989 | Nuclear Physics B, Vol. 313, No. 2
- Finitely-reducible realizations of the N = 2 superconformal algebra
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- Recent developments in string theory
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  1 January 1999 | Journal of Physics G: Nuclear and Particle Physics, Vol. 15, No. 2
- Diffeomorphism Groups And Local Symmetries: Some Applications In Quantum Physics
  Gerald A. Goldin and David H. Sharp
  1 Jan 1989
- Thirring Strings: Use of Generalized Nonabelian Bosonization Techniques
  Elcio Abdalla
  1 Jan 1989
- Recent Results in Two-Dimensional Conformal Field Theory
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  1 Jan 1989
- Coherent states and infinite-dimensional lie algebras: An outlook
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- The quantization of chiral bosons coupled to gravity
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- BRST quantization of nonabelian chiral bosons
  Robert Link
  1 Jan 1989 | Physics Letters B, Vol. 216, No. 1-2
- Path integral analysis of chiral bosonization
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  1 Jan 1989 | Nuclear Physics B, Vol. 312, No. 1
- Affine superalgebras, unitary representations and the sugawara construction
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  1 Jan 1989 | Nuclear Physics B, Vol. 313, No. 1
- References
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- FINITE TEMPERATURE 2-DIMENSIONAL QFT MODELS OF CONFORMAL CURRENT ALGEBRA*)*)The present notes are a preview of a work in progress by D.Buchholz, G.Mack and the author and are based on the lectures presented at the International School on Group Theoretical Methods, Varna, Bulgaria June 1987 and Poiana Braşov Summer School, September 1987.
  I.T. Todorov
  1 Jan 1989
- KAC-MOODY ALGEBRAS IN 2D CONFORMAL FIELD THEORIES
  Peter Bouwknegt
  1 Jan 1989
- CONFORMAL ALGEBRAS AND DEFECTS IN THE QUANTUM ISING CHAIN
  Malte Henkel
  1 Jan 1989
- A New Method of Incorporating Symmetry into Superstring Theory
  R. BLUHM, L. DOLAN and P. GODDARD
  1 Jan 1989
- A classification of contragredient lie superalgebras of finite growth
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- Higher-order Sugawara operators for affine Lie algebras
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  1 January 1989 | Transactions of the American Mathematical Society, Vol. 315, No. 1
- A presentation for the Virasoro and super-Virasoro algebras
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  1 Dec 1988 | Communications in Mathematical Physics, Vol. 117, No. 4
- Conformal deformation by the currents of affine g
  J.K Freericks and M.B Halpern
  1 Dec 1988 | Annals of Physics, Vol. 188, No. 2
- Unitary Sugawara constructions for affine superalgebras
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  1 Dec 1988 | Physics Letters B, Vol. 215, No. 4
- Two-point function on a torus for the SU(3) WZW theory
  Sudhakar Panda and Sumathi Rao
  1 Dec 1988 | Physics Letters B, Vol. 215, No. 3
- The algebraic structure of the fermionic string
  David Kutasov
  1 Dec 1988 | Nuclear Physics B, Vol. 311, No. 2
- Extended supersymmetric σ-models on group manifolds (II). Current algebras
  A. Sevrin, W. Troost, A. Van Proeyen and Ph. Spindel
  1 Dec 1988 | Nuclear Physics B, Vol. 311, No. 2
- Coset constructions and extended conformal algebras
  Peter Bowcock and Peter Goddard
  1 Dec 1988 | Nuclear Physics B, Vol. 305, No. 4
- The current algebra on the circle as a germ of local field theories
  Detlev Buchholz, Gerhard Mack and Ivan Todorov
  1 Dec 1988 | Nuclear Physics B - Proceedings Supplements, Vol. 5, No. 2
- Vertex operators for algebras and superalgebras
  Luc Frappat, Paul Sorba and Antonino Sciarrino
  1 Dec 1988 | Nuclear Physics B - Proceedings Supplements, Vol. 5, No. 2
- Integrable vertex models and extended conformal invariance
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  1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 21, No. 22
- Conformal symmetry of the Heisenberg model in two dimensions
  Wei Li
  1 Nov 1988 | Physics Letters B, Vol. 214, No. 1
- Vertex operators and Jordan fields
  L.A. Ferreira, J.F. Gomes and A.H. Zimerman
  1 Nov 1988 | Physics Letters B, Vol. 214, No. 3
- Sugawara's construction for Kac-Moody-Malcev algebras
  Edward P. Osipov
  1 Nov 1988 | Physics Letters B, Vol. 214, No. 3
- BRST invariance and gauge independence of string path-integrals
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  1 Nov 1988 | Nuclear Physics B, Vol. 309, No. 4
- Gauged Kac-Moody algebras
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  1 Oct 1988 | Letters in Mathematical Physics, Vol. 16, No. 3
- Generalised bosonic construction of Virasoro algebras
  G.V. Dunne, I.G. Halliday and P. Suranyi
  1 Oct 1988 | Physics Letters B, Vol. 213, No. 2
- Fermionic representation of the Wess-Zumino term and the chiral Schwinger model
  Ken-ichi Shizuya
  1 Oct 1988 | Physics Letters B, Vol. 213, No. 3
- N=1 super-WZW and N=1, 2, 3, 4 super-KdV models as D=2 current superfield theories
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  1 Oct 1988 | Physics Letters B, Vol. 212, No. 4
- N-Superstring vertex and the vertex operator for the emission of the superstring
  Ursula Carow-Watamura and Satoshi Watamura
  1 Oct 1988 | Nuclear Physics B, Vol. 308, No. 1
- Correlators of primary fields in the SU(2) WZW theory on Riemann surfaces
  Samir D. Mathur, Sunil Mukhi and Ashoke Sen
  1 Oct 1988 | Nuclear Physics B, Vol. 305, No. 2
- Weyl groups, supercurrents and covariant lattices
  A.N. Schellekens and N.P. Warner
  1 Oct 1988 | Nuclear Physics B, Vol. 308, No. 2-3
- Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra
  Victor Aldaya and Jose Navarro-Salas
  1 Aug 1988 | Letters in Mathematical Physics, Vol. 16, No. 2
- Marginal deformation of minimal N=2 superconformal field theories and the witten index
  Sung-Kil Yang
  1 Aug 1988 | Physics Letters B, Vol. 209, No. 2-3
- 2n-point correlation functions of the thirring model and the associated Wess-Zumino-Witten model
  Akira Fujitsu and Kazuhiro Kimura
  1 Aug 1988 | Physics Letters B, Vol. 209, No. 4
- superconformal field theory
  L. Dixon, P. Ginsparg and J. Harvey
  1 Aug 1988 | Nuclear Physics B, Vol. 306, No. 3
- Operator content of the four-state Potts quantum chain with Z 3 -boundary conditions
  U Grimm
  1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 21, No. 13
- Four-dimensional superstrings live on group manifolds
  P. Fré and F. Gliozzi
  1 Jul 1988 | Physics Letters B, Vol. 208, No. 2
- On-shell equivalence of superstrings
  A.R. Miković and W. Siegel
  1 Jul 1988 | Physics Letters B, Vol. 209, No. 1
- Operator content of n-state quantum chains in the c=1 region
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  1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 21, No. 12
- A construction of thec<1 modular invariant partition functions
  Daniel Altschuler, Korkut Bardakci and Eliezer Rabinovici
  1 Jun 1988 | Communications in Mathematical Physics, Vol. 118, No. 2
- Quantum integrability and Kac-Moody algebras
  M. Gomes, V. Kurak and A.J. Da Silva
  1 Jun 1988 | Physics Letters B, Vol. 207, No. 3
- On the “current” algebra of the KdV equation
  Ashok Das
  1 Jun 1988 | Physics Letters B, Vol. 207, No. 4
- A bosonic representation of the twisted string emission vertex
  E. Corrigan and T.J. Hollowood
  1 Jun 1988 | Nuclear Physics B, Vol. 303, No. 1
- Equations invariant under the symmetry group of the Kadomtsev-Petviashvili equation
  D. David, D. Levi and P. Winternitz
  1 May 1988 | Physics Letters A, Vol. 129, No. 3
- The cylindrical Kadomtsev-Petviashvili equation; its Kac-Moody-Virasoro algebra and relation to KP equation
  D. Levi and P. Winternitz
  1 May 1988 | Physics Letters A, Vol. 129, No. 3
- The Virasoro algebra and group in four dimensions
  Yao-Zhong Zhang
  1 May 1988 | Journal of Mathematical Physics, Vol. 29, No. 5
- Chiral Bosonization
  H. O. Girotti, M. Gomes, V. Kurak, V. O. Rivelles and A. J. da Silva
  9 May 1988 | Physical Review Letters, Vol. 60, No. 19
- Integrable non-isospectral flows associated with the Kadomtsev-Petviashvili equations in 2+1 dimensions
  Y Cheng, Y Li and R K Bullough
  1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 21, No. 8
- Orbifold compactification of heterotic string theories
  P. Bantay
  1 Apr 1988 | Physics Letters B, Vol. 203, No. 4
- Bosonization and BRST invariant three-superstring Caneschi-Schwimmer-Veneziano vertex
  Ursula Carow-Watamura and Satoshi Watamura
  1 Apr 1988 | Nuclear Physics B, Vol. 301, No. 1
- The spin structure construction of string models and multi-loop modular invariance
  H. Kawai, D.C. Lewellen, J.A. Schwartz and S.-H.H. Tye
  1 Apr 1988 | Nuclear Physics B, Vol. 299, No. 3
- Algebraic approach to the geometry of the (super-) string model
  Henrik Aratyn and Randall Ingermanson
  1 Apr 1988 | Nuclear Physics B, Vol. 299, No. 3
- Gauge symmetry enlargement and accidental massless spectrum of string models on group manifolds
  Dimitra Karabali and Howard J. Schnitzer
  1 Apr 1988 | Nuclear Physics B, Vol. 299, No. 3
- Construction of classical Virasoro algebras as SU(1,1) extensions
  D.B. Fairlie, J. Nuyts and C.K. Zachos
  1 Mar 1988 | Physics Letters B, Vol. 202, No. 3
- Non-abelian bosonization in higher genus Riemann surfaces
  I.G. Koh and M. Yu
  1 Mar 1988 | Physics Letters B, Vol. 203, No. 3
- A string construction of a commutative non-associative algebra related to the exceptional Jordan algebra
  E. Corrigan and T.J. Hollowood
  1 Mar 1988 | Physics Letters B, Vol. 203, No. 1-2
- Superconformal invariant non-linear σ-models from the bosonic ones
  M. Gomes, V. Kurak and A.J. Da Silva
  1 Mar 1988 | Physics Letters B, Vol. 202, No. 4
- String models with c < 1 components
  K. Bardakci, E. Rabinovici and B. Säring
  1 Mar 1988 | Nuclear Physics B, Vol. 299, No. 1
- Conformal invariance and line defects in the two-dimensional Ising model
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- Integrable quantum field theories and conformal field theories from lattice models in the light-cone approach
  C. Destri and H.J. de Vega
  1 Feb 1988 | Physics Letters B, Vol. 201, No. 2
- Weyl fields, quantum integrability and conformal invariant field theories
  M. Gomes, V. Kurak and A.J. Da Silva
  1 Feb 1988 | Nuclear Physics B, Vol. 295, No. 2
- Curiosities at c = 1
  P. Ginsparg
  1 Feb 1988 | Nuclear Physics B, Vol. 295, No. 2
- The Kac-moody and Virasoro commutation equations
  Belal E. Baaquie
  1 Feb 1988 | Nuclear Physics B, Vol. 295, No. 2
- Liouville superstring and Ising model in three dimensions
  Adel Bilal and Jean-Loup Gervais
  1 Feb 1988 | Nuclear Physics B, Vol. 295, No. 2
- Loop algebras and superalgebras based on S 7
  F. Englert, A. Sevrin, W. Troost, A. Van Proeyen and Ph. Spindel
  1 Feb 1988 | Journal of Mathematical Physics, Vol. 29, No. 2
- Introduction to Conformal Invariant Quantum Field Theory in Two and More Dimensions
  Gerhard Mack
  1 Jan 1988
- Generalization of the Sugawara Construction
  Jean Thierry-Mieg
  1 Jan 1988
- Two-Dimensional Supergravities, Hidden Symmetries and Integrable Systems
  Hermann Nicolai
  1 Jan 1988
- Spacetime Couplings and Affine Algebras
  Paul Ginsparg
  1 Jan 1988
- Modular Invariance and Infinite-Dimensional Algebras
  Peter Goddard
  1 Jan 1988
- Type II Superstrings in Four Dimensions
  John H. Schwarz
  1 Jan 1988
- Liouville Strings
  Jean-Loup Gervais
  1 Jan 1988
- Conformal Field Theory and Kac-Moody Algebras
  Michio Kaku
  1 Jan 1988
- Soliton Statistical Mechanics: Statistical Mechanics of the Quantum and Classical Integrable Models
  R. K. Bullough, D. J. Pilling and J. Timonen
  1 Jan 1988
- Homogeneous space construction of Modular Invariant QFT models with a chiral U(1) current
  R. P. Paunov and I. T. Todorov
  1 Jan 1988
- Fermions and Jordan matrices
  Henri Ruegg
  1 Jan 1988
- Anomalies as curvature in complex geometry
  M.J. Bowick and S.G. Rajeev
  1 Jan 1988 | Nuclear Physics B, Vol. 296, No. 4
- Higher spin conserved currents in c = 1 conformally invariant systems
  M. Baake, P. Christe and V. Rittenberg
  1 Jan 1988 | Nuclear Physics B, Vol. 300
- Comments on the algebra of straight, twisted and intertwining vertex operators
  E. Corrigan and T.J. Hollowood
  1 Jan 1988 | Nuclear Physics B, Vol. 304
- Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants
  F.A. Bais, P. Bouwknegt, M. Surridge and K. Schoutens
  1 Jan 1988 | Nuclear Physics B, Vol. 304
- Coset construction for extended Virasoro algebras
  F.A. Bais, P. Bouwknegt, M. Surridge and K. Schoutens
  1 Jan 1988 | Nuclear Physics B, Vol. 304
- Bibliography
  1 Jan 1988
- Superalgebras, symplectic bosons and the Sugawara construction
  P. Goddard, D. Olive and G. Waterson
  1 Dec 1987 | Communications in Mathematical Physics, Vol. 112, No. 4
- String quantization on group manifolds and the holomorphic geometry of DiffS 1/S 1
  Jouko Mickelsson
  1 Dec 1987 | Communications in Mathematical Physics, Vol. 112, No. 4
- Group theoretical quantization on loop spaces and the sugawara construction
  I. Bakas and D. McMullan
  1 Dec 1987 | Physics Letters B, Vol. 199, No. 3
- Boson realisation of Virasoro and Kac-Moody algebras and their indecomposable representations
  Chang-Pu Sun
  1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 20, No. 17
- Quantum geometry of a conformal field theory
  Mihaela Niculescu Sanielevici and Gordon W. Semenoff
  1 Nov 1987 | Physics Letters B, Vol. 198, No. 2
- Gauge and gravitational couplings in four-dimensional string theories
  P. Ginsparg
  1 Oct 1987 | Physics Letters B, Vol. 197, No. 1-2
- Modular invariant QFT models of u(1) conformal current algebra
  Roman R. Paunov and Ivan T. Todorov
  1 Oct 1987 | Physics Letters B, Vol. 196, No. 4
- New Virasoro and Kac-Moody symmetries for the non-linear σ-model
  B Hou and W Li
  1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 20, No. 14
- Fermions and octonions
  P. Goddard, W. Nahm, D. I. Olive, H. Ruegg and A. Schwimmer
  1 Sep 1987 | Communications in Mathematical Physics, Vol. 112, No. 3
- Formal Group Laws for Affine Kac-Moody groups and group quantization
  Victor Aldaya and Jose Navarro-Salas
  1 Sep 1987 | Communications in Mathematical Physics, Vol. 113, No. 3
- A connection between the twisted N = 2 superconformal and SU(2) Kac-moody algebras
  V. Rittenberg and A. Schwimmer
  1 Sep 1987 | Physics Letters B, Vol. 195, No. 2
- Anomalous current algebras in the Skyrme model or chiral G×G with Wess-Zumino term
  A.C. Davis, J.A. Gracey and A.J. Macfarlane
  1 Aug 1987 | Physics Letters B, Vol. 194, No. 3
- Non-Abelian bosonization: Stress-energy correlation functions
  Lowell S. Brown, Gary J. Goldberg, Chaiho P. Rim and Rafael I. Nepomechie
  15 July 1987 | Physical Review D, Vol. 36, No. 2
- Kac-Moody symmetry of generalized non-linear Schr�dinger equations
  A. D. W. B. Crumey
  1 Jun 1987 | Communications in Mathematical Physics, Vol. 111, No. 2
- Representations of Kac-Moody and Virasoro Algebras
  Peter Goddard†
  1 Jan 1987
- The five-dimensional open Liouville superstring
  Adel Bilal and Jean-Loup Gervais
  1 Jan 1987 | Nuclear Physics B, Vol. 293
- Twisted chiral models with Wess-Zumino terms, and strings
  M. Forger and P. Zizzi
  1 Jan 1987 | Nuclear Physics B, Vol. 287
- Conformal embeddings and hidden symmetries of free fermion theories
  Jürgen Fuchs
  1 Jan 1987 | Nuclear Physics B, Vol. 290
- On the construction of modular invariant partition functions
  Peter Bouwknegt
  1 Jan 1987 | Nuclear Physics B, Vol. 290
- Conformal techniques, bosonization and tree-level string amplitudes
  V. Alan Kostelecký, Olaf Lechtenfeld, Wolfgang Lerche, Stuart Samuel and Satoshi Watamura
  1 Jan 1987 | Nuclear Physics B, Vol. 288
- Critical exponents of defective Ising models and the U(1) Kac-Moody-Virasoro algebras
  Malte Henkel and András Patkós
  1 Jan 1987 | Nuclear Physics B, Vol. 285
- Conformal subalgebras and symmetric spaces
  R.C. Arcuri, J.F. Gomes and D.I. Olive
  1 Jan 1987 | Nuclear Physics B, Vol. 285
- Virasoro algebras with central charge c < 1
  P. Bowcock and P. Goddard
  1 Jan 1987 | Nuclear Physics B, Vol. 285
- Bosons, fermions and Thirring strings
  Jonathan Bagger, Dennis Nemeschansky, Nathan Seiberg and Shimon Yankielowicz
  1 Jan 1987 | Nuclear Physics B, Vol. 289
- A new method of incorporating symmetry into superstring theory
  R. Bluhm, L. Dolan and P. Goddard
  1 Jan 1987 | Nuclear Physics B, Vol. 289
- Bose-Fermi equivalence of the two-dimensional torus for simply-laced groups
  A.N. Redlich, Howard J. Schnitzer and K. Tsokos
  1 Jan 1987 | Nuclear Physics B, Vol. 289
- Covariant higher spin vertex operators in the Ramond sector
  I.G. Koh, W. Troost and A. Van Proeyen
  1 Jan 1987 | Nuclear Physics B, Vol. 292
- Algebras, Lattices and Strings 1986
  David Olive
  15 February 2007 | Physica Scripta, Vol. T15
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KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS

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