Conformal field theory

Gawędzki, Krzysztof

Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 704, 32 p.

@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, dans Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 704, 32 p. http://www.numdam.org/item/SB_1988-1989__31__95_0/

Bibliographie
Cité par

[1] L. Alvarez-Gaume, C. Gomez, G. Moore, C. Vafa - Strings in the operator formalism, Nucl. Phys. B 303, 455-521 (1988). | MR

[2] G. Anderson, G. Moore - Rationality in conformal field theory, Commun. Math. Phys. 117, 441-450 (1988). | MR | Zbl

[3] E. Artin - 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] M. F. Atiyah, R. Bott - The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. Lond. A 308, 523-615 (1982). | MR | Zbl

[5] R. J. Baxter - Ezactly Solved Models in Statistical Mechanics, Academic Press, London 1982. | MR | Zbl

[6] A. A. Belavin, A. M. Polyakov, A. B. Zamolodchikov - Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241, 333-380 (1984). | MR | Zbl

[7] D. Bernard - On the Wess-Zumino-Witten models on Riemann surfaces, Nucl. Phys. B 309,145-174 (1988). | MR

[8] A. Bilal, J.-L. Gervais - Systematic approach to conformal systems with extended Virasoro symmetries, Phys. Lett. B 206, 412-420 (1988). | MR

[9] A. Bilal, J.-L. Gervais - Systematic construction of conformal theories with higher-spin Virasoro symmetries, LPTENS 88/24 preprint. | MR

[10] J.-B. Bost - 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] R. Brustein, Y. Ne'Eman, S. Sternberg - Duality, crossing and Mac Lane's coherence, TAUP-1669-88 and N-190-88 preprint.

[12] R. Brustein, S. Yankielowicz, J.-B. Zuber - Factorization and selection rules of operator product algebras in conformal field theories, SPhT/88-086 and TAUP-1647-88 preprint. | MR

[13] A. Cappelli, C. Itzykson, J.-B. Zuber - Modular invariant partition functions in two dimensions, Nucl. Phys. B 280 [FS 18], 445-465 (1987). | MR | Zbl

[14] A. Cappelli, C. Itzykson, J.-B. Zuber - The A-D-E classification of minimal and A1(1) conformal invariant theories, Commun. Math. Phys. 113, 1-26 (1987). | MR | Zbl

[15] J. L. Cardy - Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 [FS 16], 186-204 (1986). | MR | Zbl

[16] E. Charpentier, K. Gawędzki, in preparation.

[17] S. K. Donaldson - A new proof of a theorem of Narasimhan and Seshadri, J. Diff. Geom. 18, 269-277 (1983). | MR | Zbl

[18] S. K. Donaldson - Infinite determinants, stable bundles and curvature, Duke Math. J. 54, 231-247 (1987). | MR | Zbl

[19] V. S. Dotsenko, V. A. Fateev - Conformal algebra and multipoint correlation functions in 2d statistical models, Nucl. Phys. B 240 [FS 12], 312-348 (1984). | MR

[20] V. S. Dotsenko, V. A. Fateev - 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] T. Eguchi, H. Ooguri - Conformal and current algebras on a general Riemann surface, Nucl. Phys. B 282, 308-328 (1987). | MR

[22] B. L. Feigin, D. B. Fuchs - Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra, Funct. Anal. Appl. 16, 114-126 (1982). | Zbl

[23] B. L. Feigin, D. B. Fuchs - Verma modules over the Virasoro algebra, Funct. Anal. Appl. 17, 241-242 (1983). | MR | Zbl

[24] G. Felder, K. Gawędzki, A. Kupiainen - Spectra of Wess-Zumino-Witten models with arbitrary simple groups, Commun. Math. Phys. 117, 127-158 (1988). | MR | Zbl

[25] I. B. Frenkel - 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] I. B. Frenkel - talk at the International Congress of Mathematical Physics, Swansea 1988.

[27] I. B. Frenkel, J. Lepowsky, A. Meurman - 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] D. Friedan, E. Martinec, S. Shenker - Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271, 93-165 (1986). | MR

[29] D. Friedan, Z. Qiu, S. Shenker - Conformal invariance, unitarity and critical ezponents in two dimensions, Phys. Rev. Lett. 52, 1575-1578 (1984). | MR

[30] D. Friedan, Z. Qiu, S. Shenker - Details of the non-unitarity proof for highest weight representations of the Virasoro algebra, Commun. Math. Phys. 107, 535-542 (1986). | MR | Zbl

[31] D. Friedan, S. Shenker - The integrable analytic geometry of quantum string, Phys. Lett. B 175, 287-296 (1986). | MR

[32] D. Friedan, S. Shenker - The analytic geometry of two-dimensional conformal field theory, Nucl. Phys. B 281, 509-545 (1987). | MR

[33] J. Fröhlich - 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] J. Fröhlich - On the structure of (unitary) rational conformal field theory, ETH preprint 1988. | MR

[35] H. Garland - The arithmetic theory of loop algebras, J. Algebra 53, 480-551 (1978). | MR | Zbl

[36] K. Gawędzki, A. Kupiainen - G/H conformal field theory from gauged WZW model, Phys. Lett. B, to appear. | MR

[37] K. Gawędzki, A. Kupiainen - Coset construction from functional integral, IHES/P/88/45 preprint. | MR

[38] I. M. Gelfand, D. B. Fuchs - The cohomologies of the Lie algebra of the vector fields in a circle, Funct. Anal. Appl. 2, 342-343 (1968). | Zbl

[39] D. Gepner - On the spectrum of 2d conformal field theories, Nucl. Phys. B 287, 111-130 (1987). | MR

[40] D. Gepner - String theory on Calabi-Yau manifolds: the three generation case, Princeton preprint 1988.

[41] D. Gepner, Z. Qiu - Modular invariant partition functions for parafermionic field theories, Nucl. Phys. B 285 [FS 19], 423-453 (1987). | MR

[42] D. Gepner, E. Witten - String theory on group manifolds, Nucl. Phys. B 278, 493-549 (1986). | MR

[43] P. Goddard, A. Kent, D. Olive - Virasoro algebras and coset space models, Phys. Lett. B 152, 88-92 (1985). | MR | Zbl

[44] P. Goddard, A. Kent, D. Olive - Unitary representations of the Virasoro and super-Virasoro algebras, Commun. Math. Phys. 103, 105-119 (1986). | MR | Zbl

[45] R. Goodman, N. R. Wallach - 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] R. Goodman, N. R. Wallach - Projective unitary positive-energy representations of Diff(S1), J. Func. Anal. 63, 299-321 (1985). | MR | Zbl

[47] M. B. Green, J. H. Schwarz, E. Witten - Superstring Theory, Vol. 1 and 2, Cambridge University Press, Cambridge 1987. | MR | Zbl

[48] D. J. Gross, J. A. Harvey, E. Martinec, R. Rohm - 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] J. Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72, 221-239 (1983). | MR | Zbl

[50] M. Jimbo, T. Miwa, M. Okado - Local state probabilities of solvable lattice models: An A(1)n-1 family, Nucl. Phys. B 300 [FS 22], 74-108 (1988). | MR

[51] V. F. R. Jones - Hecke algebra representations of braid groups and link polynomials, Ann. Math. 126, 335-388 (1987). | MR | Zbl

[52] V. G. Kac - Highest weight representations of infinite-dimensional Lie algebras, Proceedings of the International Congress of Mathematicians, Helsinki 1978, pp. 299-304. | MR | Zbl

[53] V. G. Kac - Infinite-dimensional Lie algebras and Dedekind's η - function, Funct. Anal. Appl. 8, 68-70 (1974). | Zbl

[54] A. Kato - Classification of modular invariant partition functions in two dimensions, Mod. Phys. Lett. A 2, 585-600 (1987). | MR

[55] V. Knizhnik, A. B. Zamolodchikov - Current algebra and Wess-Zumino model in two dimensions, Nucl. Phys. B 247, 83-103 (1984). | MR | Zbl

[56] T. Kohno - Linear representations of braid groups and classical Yang-Baxter equations, in Artin's Braid Groups, Contemporary Mathematics, to appear. | MR | Zbl

[57] I. M. Krichever - Integration of non-linear equations by methods of algebraic geometry, Funct. Anal. Appl. 11, 12-26 (1977). | Zbl

[58] M. Lüscher, G. Mack, unpublished manuscript, 1976.

[59] J. W. Milnor - 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] G. Moore, N. Seiberg - Polynomial equations for rational conformal field theories, Phys. Lett. B 212, 451-460 (1988). | MR

[61] G. Moore, N. Seiberg - Naturality in conformal field theory, IASSNS-HEP-88/31 preprint. | MR

[62] G. Moore, N. Seiberg - Classical and quantum conformal field theory, IASSNS-HEP- 88/39 preprint. | MR

[63] W. Nahm - Quantum field theories in one and two dimensions, Duke Math. J. 54, 579-613 (1987). | MR | Zbl

[64] W. Nahm - Lie group exponents and SU(2) current algebras, Commun. Math. Phys. 118, 171-176 (1988). | MR | Zbl

[65] M. S. Narasimhan, C. S. Seshadri - Stable and unitary vector bundles on a compact Riemann surface, Ann. Math. 82, 540-567 (1965). | MR | Zbl

[66] V. Pasquier - Continuum limit of lattice models built on quantum groups, Nucl. Phys. B 295 [FS 21], 491-510 (1988). | MR

[67] A. M. Polyakov - Conformal symmetry of critical fluctuations, JETP Lett. 12, 381-383 (1970).

[68] A. Pressley, G. Segal - Loop Groups, Clarendon Press, Oxford 1986. | MR | Zbl

[69] D. Quillen - Determinants of Cauchy-Riemann operators over a Riemanri surface, Funct. Anal. Appl. 19, 31-34 (1985). | MR | Zbl

[70] D. B. Ray, I. M. Singer - Analytic torsion for complex manifolds, Ann. Math. 98,154-177 (1973). | MR | Zbl

[71] A. Rocha-Caridi - 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] K.-H. Rehren - Locality of conformal fields in two dimensions: exchange algebra on the light-cone, Commun. Math. Phys. 116, 675-688 (1988). | MR | Zbl

[73] K.-H. Rehren, B. Schroer - Einstein causality and Artin braids, Freie Universität Berlin preprint, 1988. | MR

[74] B. Schroer - Operator approach to conformal invariant quantum field theories and related problems, Nucl. Phys. B 295 [FS 21], 586-616 (1988). | MR

[75] G. Segal - The definitions of conformal field theory, in Links Between Geometry and Mathematical Physics, pp. 13-17. MPI/87-58 preprint. | MR

[76] G. Segal - talk at the International Congress of Mathematical Physics, Swansea 1988.

[77] J.-P. Serre - Cours d'Arithmétique, Presses Universitaires de France, Paris 1970. | MR | Zbl

[78] H. Sugawara - A field theory of currents, Phys. Rev. 170, 1659-1662 (1968).

[79] J. Tits - 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] C. Vafa - Operator formulation on Riemann surface, Phys. Lett. B 190, 47-54 (1987). | MR

[81] C. Vafa - Conformal theories and punctured surfaces, Phys. Lett. B 199, 195-202 (1987). | MR

[82] C. Vafa - Towards classification of conformal theories, Phys. Lett. B 206, 421-426 (1988). | MR

[83] C. Vafa - c-theorem and the topology of 2d QFT's, Phys. Lett. B 212, 28-32 (1988). | MR

[84] J.-L. Verdier - Groupes quantique [d'après V. G. Drinfeld], Sém. Bourbaki, Juin 1987, Astérisque 152-153, 305-319 (1987). | Numdam | MR | Zbl

[85] E. Verlinde - Fusion rules and modular transformations in 2d conformal field theory, Nucl. Phys. B 300 [FS 22], 360-376 (1988). | MR | Zbl

[86] E. Witten - Non-abelian bosonization in two dimensions, Commun. Math. Phys. 92, 455-472 (1984). | Zbl

[87] E. Witten - 2+1 dimensional gravity as an exactly soluble system, IASSNS-HEP-88/ preprint. | MR

[88] E. Witten - Quantum field theory and the Jones polynomial, IASSNS-HEP-88/33 preprint.

[89] A. B. Zamolodchikov - Renormalization group and perturbation theory near fixed points in two-dimensional field theory, Yad. Fiz. 46, 1819-1831 (1987). | MR