@incollection{SB_1988-1989__31__95_0, author = {Gaw\k{e}dzki, Krzysztof}, title = {Conformal field theory}, booktitle = {S\'eminaire Bourbaki : volume 1988/89, expos\'es 700-714}, series = {Ast\'erisque}, note = {talk:704}, pages = {95--126}, publisher = {Soci\'et\'e math\'ematique de France}, number = {177-178}, year = {1989}, mrnumber = {1040570}, zbl = {0699.53085}, language = {en}, url = {http://www.numdam.org/item/SB_1988-1989__31__95_0/} }
TY - CHAP AU - Gawędzki, Krzysztof TI - Conformal field theory BT - Séminaire Bourbaki : volume 1988/89, exposés 700-714 AU - Collectif T3 - Astérisque N1 - talk:704 PY - 1989 SP - 95 EP - 126 IS - 177-178 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1988-1989__31__95_0/ LA - en ID - SB_1988-1989__31__95_0 ER -
%0 Book Section %A Gawędzki, Krzysztof %T Conformal field theory %B Séminaire Bourbaki : volume 1988/89, exposés 700-714 %A Collectif %S Astérisque %Z talk:704 %D 1989 %P 95-126 %N 177-178 %I Société mathématique de France %U http://www.numdam.org/item/SB_1988-1989__31__95_0/ %G en %F SB_1988-1989__31__95_0
Gawędzki, Krzysztof. Conformal field theory, in Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Talk no. 704, 32 p. http://www.numdam.org/item/SB_1988-1989__31__95_0/
[1] Strings in the operator formalism, Nucl. Phys. B 303, 455-521 (1988). | MR
, , , -[2] Rationality in conformal field theory, Commun. Math. Phys. 117, 441-450 (1988). | MR | Zbl
, -[3] The theory of braids, in Collected Papers, pp. 491-498, S. Lang et al. (eds.), Addison-Wesley, Reading MA, Palo Alto, London, Dallas, Atlanta 1965. | MR
-[4] The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. Lond. A 308, 523-615 (1982). | MR | Zbl
, -[5] Ezactly Solved Models in Statistical Mechanics, Academic Press, London 1982. | MR | Zbl
-[6] Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241, 333-380 (1984). | MR | Zbl
, , -[7] On the Wess-Zumino-Witten models on Riemann surfaces, Nucl. Phys. B 309,145-174 (1988). | MR
-[8] Systematic approach to conformal systems with extended Virasoro symmetries, Phys. Lett. B 206, 412-420 (1988). | MR
, -[9] Systematic construction of conformal theories with higher-spin Virasoro symmetries, LPTENS 88/24 preprint. | MR
, -[10] Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes, Sém. Bourbaki, Fév. 1987, exp. 676, Astérisque 152-153, 113-149 (1987). | Numdam | MR | Zbl
-[11] Duality, crossing and Mac Lane's coherence, TAUP-1669-88 and N-190-88 preprint.
, , -[12] Factorization and selection rules of operator product algebras in conformal field theories, SPhT/88-086 and TAUP-1647-88 preprint. | MR
, , -[13] Modular invariant partition functions in two dimensions, Nucl. Phys. B 280 [FS 18], 445-465 (1987). | MR | Zbl
, , -[14] The A-D-E classification of minimal and A1(1) conformal invariant theories, Commun. Math. Phys. 113, 1-26 (1987). | MR | Zbl
, , -[15] Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 [FS 16], 186-204 (1986). | MR | Zbl
-[16]
, , in preparation.[17] A new proof of a theorem of Narasimhan and Seshadri, J. Diff. Geom. 18, 269-277 (1983). | MR | Zbl
-[18] Infinite determinants, stable bundles and curvature, Duke Math. J. 54, 231-247 (1987). | MR | Zbl
-[19] Conformal algebra and multipoint correlation functions in 2d statistical models, Nucl. Phys. B 240 [FS 12], 312-348 (1984). | MR
, -[20] Four-point correlation functions and operator algebra in 2d conformal invariant theories with central charge c ≤ 1, Nucl. Phys. B 251 [FS 13], 691-734 (1985).
, -[21] Conformal and current algebras on a general Riemann surface, Nucl. Phys. B 282, 308-328 (1987). | MR
, -[22] Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra, Funct. Anal. Appl. 16, 114-126 (1982). | Zbl
, -[23] Verma modules over the Virasoro algebra, Funct. Anal. Appl. 17, 241-242 (1983). | MR | Zbl
, -[24] Spectra of Wess-Zumino-Witten models with arbitrary simple groups, Commun. Math. Phys. 117, 127-158 (1988). | MR | Zbl
, , -[25] Two constructions of affine Lie algebra representations and Boson-Fermion correspondence in quantum field theory, J. Func. Anal. 44, 259-327 (1981). | MR | Zbl
-[26] talk at the International Congress of Mathematical Physics, Swansea 1988.
-[27] A moonshine module for the Monster, in Vertex Operators in Mathematics and Physics, J. Lepowsky et al. (eds.), MSRI Publications No. 3, pp. 231-273, Springer, Berlin, Heidelberg, New York 1984. | MR | Zbl
, , -[28] Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271, 93-165 (1986). | MR
, , -[29] Conformal invariance, unitarity and critical ezponents in two dimensions, Phys. Rev. Lett. 52, 1575-1578 (1984). | MR
, , -[30] Details of the non-unitarity proof for highest weight representations of the Virasoro algebra, Commun. Math. Phys. 107, 535-542 (1986). | MR | Zbl
, , -[31] The integrable analytic geometry of quantum string, Phys. Lett. B 175, 287-296 (1986). | MR
, -[32] The analytic geometry of two-dimensional conformal field theory, Nucl. Phys. B 281, 509-545 (1987). | MR
, -[33] Statistics of fields, the Yang-Baxter equation and the theory of knots and links, lectures at Cargèse 1987, to appear in Nonperturbative Quantum Field Theory, G.'t Hooft et al. (eds.), Plenum, New York. | MR
-[34] On the structure of (unitary) rational conformal field theory, ETH preprint 1988. | MR
-[35] The arithmetic theory of loop algebras, J. Algebra 53, 480-551 (1978). | MR | Zbl
-[36] G/H conformal field theory from gauged WZW model, Phys. Lett. B, to appear. | MR
, -[37] Coset construction from functional integral, IHES/P/88/45 preprint. | MR
, -[38] The cohomologies of the Lie algebra of the vector fields in a circle, Funct. Anal. Appl. 2, 342-343 (1968). | Zbl
, -[39] On the spectrum of 2d conformal field theories, Nucl. Phys. B 287, 111-130 (1987). | MR
-[40] String theory on Calabi-Yau manifolds: the three generation case, Princeton preprint 1988.
-[41] Modular invariant partition functions for parafermionic field theories, Nucl. Phys. B 285 [FS 19], 423-453 (1987). | MR
, -[42] String theory on group manifolds, Nucl. Phys. B 278, 493-549 (1986). | MR
, -[43] Virasoro algebras and coset space models, Phys. Lett. B 152, 88-92 (1985). | MR | Zbl
, , -[44] Unitary representations of the Virasoro and super-Virasoro algebras, Commun. Math. Phys. 103, 105-119 (1986). | MR | Zbl
, , -[45] Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle, J. Reine Angew. Math. 347, 69-133 (1984). | MR | Zbl
, -[46] Projective unitary positive-energy representations of Diff(S1), J. Func. Anal. 63, 299-321 (1985). | MR | Zbl
, -[47] Superstring Theory, Vol. 1 and 2, Cambridge University Press, Cambridge 1987. | MR | Zbl
, , -[48] Heterotic string theory (I). The free heterotic string, Nucl. Phys. B 256, 253-284 (1985), (II). The interacting heterotic string, Nucl. Phys. B 267, 75-124 (1986). | MR
, , , -[49] The second homology group of the mapping class group of an orientable surface, Invent. Math. 72, 221-239 (1983). | MR | Zbl
,[50] Local state probabilities of solvable lattice models: An A(1)n-1 family, Nucl. Phys. B 300 [FS 22], 74-108 (1988). | MR
, , -[51] Hecke algebra representations of braid groups and link polynomials, Ann. Math. 126, 335-388 (1987). | MR | Zbl
-[52] Highest weight representations of infinite-dimensional Lie algebras, Proceedings of the International Congress of Mathematicians, Helsinki 1978, pp. 299-304. | MR | Zbl
-[53] Infinite-dimensional Lie algebras and Dedekind's η - function, Funct. Anal. Appl. 8, 68-70 (1974). | Zbl
-[54] Classification of modular invariant partition functions in two dimensions, Mod. Phys. Lett. A 2, 585-600 (1987). | MR
-[55] Current algebra and Wess-Zumino model in two dimensions, Nucl. Phys. B 247, 83-103 (1984). | MR | Zbl
, -[56] Linear representations of braid groups and classical Yang-Baxter equations, in Artin's Braid Groups, Contemporary Mathematics, to appear. | MR | Zbl
-[57] Integration of non-linear equations by methods of algebraic geometry, Funct. Anal. Appl. 11, 12-26 (1977). | Zbl
-[58]
, , unpublished manuscript, 1976.[59] Remarks on infinite dimensional Lie groups, in Relativity, Groups and Topology II, Les Houches Session XL, B.S. de Witt et al. (eds.), North-Holland, Amsterdam 1984. | MR | Zbl
-[60] Polynomial equations for rational conformal field theories, Phys. Lett. B 212, 451-460 (1988). | MR
, -[61] Naturality in conformal field theory, IASSNS-HEP-88/31 preprint. | MR
, -[62] Classical and quantum conformal field theory, IASSNS-HEP- 88/39 preprint. | MR
, -[63] Quantum field theories in one and two dimensions, Duke Math. J. 54, 579-613 (1987). | MR | Zbl
-[64] Lie group exponents and SU(2) current algebras, Commun. Math. Phys. 118, 171-176 (1988). | MR | Zbl
-[65] Stable and unitary vector bundles on a compact Riemann surface, Ann. Math. 82, 540-567 (1965). | MR | Zbl
, -[66] Continuum limit of lattice models built on quantum groups, Nucl. Phys. B 295 [FS 21], 491-510 (1988). | MR
-[67] Conformal symmetry of critical fluctuations, JETP Lett. 12, 381-383 (1970).
-[68] Loop Groups, Clarendon Press, Oxford 1986. | MR | Zbl
, -[69] Determinants of Cauchy-Riemann operators over a Riemanri surface, Funct. Anal. Appl. 19, 31-34 (1985). | MR | Zbl
-[70] Analytic torsion for complex manifolds, Ann. Math. 98,154-177 (1973). | MR | Zbl
, -[71] Vacuum vector representations of the Virasoro algebra, in Vertex Operators in Mathematics and Physics, J. Lepowsky et al. (eds.), MSRI Publications No. 3, pp. 451-473, Springer, Berlin, Heidelberg, New York 1984. | MR | Zbl
-[72] Locality of conformal fields in two dimensions: exchange algebra on the light-cone, Commun. Math. Phys. 116, 675-688 (1988). | MR | Zbl
-[73] Einstein causality and Artin braids, Freie Universität Berlin preprint, 1988. | MR
, -[74] Operator approach to conformal invariant quantum field theories and related problems, Nucl. Phys. B 295 [FS 21], 586-616 (1988). | MR
-[75] The definitions of conformal field theory, in Links Between Geometry and Mathematical Physics, pp. 13-17. MPI/87-58 preprint. | MR
-[76] talk at the International Congress of Mathematical Physics, Swansea 1988.
-[77] Cours d'Arithmétique, Presses Universitaires de France, Paris 1970. | MR | Zbl
-[78] A field theory of currents, Phys. Rev. 170, 1659-1662 (1968).
-[79] Le module de "moonshine" [d'après I. Frenkel, J. Lepowsky et A. Meurman], Sém. Bourbaki, Juin 1987, exp. 684, Astérisque 152-153, 285-303 (1987). | Numdam | MR | Zbl
-[80] Operator formulation on Riemann surface, Phys. Lett. B 190, 47-54 (1987). | MR
-[81] Conformal theories and punctured surfaces, Phys. Lett. B 199, 195-202 (1987). | MR
-[82] Towards classification of conformal theories, Phys. Lett. B 206, 421-426 (1988). | MR
-[83] c-theorem and the topology of 2d QFT's, Phys. Lett. B 212, 28-32 (1988). | MR
-[84] Groupes quantique [d'après V. G. Drinfeld], Sém. Bourbaki, Juin 1987, Astérisque 152-153, 305-319 (1987). | Numdam | MR | Zbl
-[85] Fusion rules and modular transformations in 2d conformal field theory, Nucl. Phys. B 300 [FS 22], 360-376 (1988). | MR | Zbl
-[86] Non-abelian bosonization in two dimensions, Commun. Math. Phys. 92, 455-472 (1984). | Zbl
-[87] 2+1 dimensional gravity as an exactly soluble system, IASSNS-HEP-88/ preprint. | MR
-[88] Quantum field theory and the Jones polynomial, IASSNS-HEP-88/33 preprint.
-[89] Renormalization group and perturbation theory near fixed points in two-dimensional field theory, Yad. Fiz. 46, 1819-1831 (1987). | MR
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