Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes
Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque, no. 152-153 (1987), Exposé no. 676, 37 p.
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Bost, Jean-Benoît. Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes, dans Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque, no. 152-153 (1987), Exposé no. 676, 37 p. http://www.numdam.org/item/SB_1986-1987__29__113_0/

[1] O. Alvarez - Theory of strings with boundaries : fluctuation, topology and quantum geometry, Nucl. Phys. B 216, 125-184 (1983). | MR

[2] O. Alvarez - Conformal anomalies and the index theorem, UCB Preprint, Ph T/85-39 (à paraître dans Nucl. Phys.). | MR

[3] L. Alvarez-Gaume, J.-B. Bost, G. Moore, Ph. Nelson et C. Vafa - Bosonization in arbitrary genus, Phys. Lett. B 178, 41-47 (1986). | MR

[4] M. F. Atiyah et I. M. Singer - Dirac operators coupled to vector potentials, Proc. Nat. Acad. Sci. 81, 2597 (1984). | MR | Zbl

[5] M. A. Baranov et A. S. Shvarts - Multiloop contribution to string theory, Pisma ZETP 42, 340-342 (1985) [= JETP Letters 42, 419-421 (1985)]. | MR

[6] A. A. Beillinson et Yu. I. Manin - The Mumford form and the Polyakov measure in string theory, Comm. Math. Physics 107, 359-376 (1986). | MR | Zbl

[7] A. A. Belavin et V. G. Knizhnik - Algebraic geometry and the geometry of quantum strings, Phys. Lett. B, 168, 201-211 (1986). | MR | Zbl

[8] A. A. Belavin et V. G. Knizhnik - Complex geometry and theory of quantum strings, Landau Institute Preprint (1986). | MR

[9] A. A. KnizhnikV. G. Knizhnik, A. Morozov, A. Perelomov - Two- and three-loop amplitudes in the bosonic string theory, Landau Institute Preprint (1986). | MR

[10] L. Bers - Finite dimensional Teichmüller spaces and generalizations, Bulletin Amer. Math. Soc. (N.S.) 5 (1981), 131-172. | MR | Zbl

[11] J.-M. Bismut - The Atiyah - Singer index theorem for families of Dirac operators : two heat equation proofs, Invent. Math. 83, 91-151 (1986). | MR | Zbl

[12] J.-M. Bismut et D. S. Freed - The analysis of elliptic families I, II, Comm. Math. Phys. 106, 159-176 (1986) et 107, 103-163 (1986). | Zbl

[ 13] J.-B. Bost et Th. Jolicoeur - A holomorphy property and the critical dimension in string theory from an index theorem, Phys. Lett. B 174, 273-276 (1986). | MR

[14] R. Bott et S. S. Chern - Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic cross sections, Acta Math. 114, 71-112 (1968). | MR | Zbl

[15] R. Catenacci, M. Cornalba, M. Martinelli et C. Reina - Algebraic geometry and path integrals for closed strings, Phys. Lett. B 172, 328-332 (1986). | MR

[16] E. D'Hoker and D. H. Phong - Multiloop amplitudes for the bosonic Polyakov string, Nuclear Physics B 269, 205-234 (1986). | MR

[ 17] S. K. Donaldson - Infinite determinants, stable bundles and curvatures, Preprint. | MR

[18] J. Fay - Analytic torsion and Prym differentials. Riemann surfaces and related topics, Proc. of the 1978 Stony Brook Conférence, Princeton University Press 1980, 107-122. | MR | Zbl

[19] D. S. Freed - Determinants, torsion and strings, Comm. Math. Phys. 107, 483-513 (1986). | MR | Zbl

[20] D. Fried - Analytic torsion and closed geodesics on hyperbolic manifolds, Invent. Math. 84, 523-540 (1986). | MR | Zbl

[21] D. Friedan - Introduction to Polyakov's string theory, in Recent advances in field theory and statistical mechanics, Les Houches 1982, J.-B. Zuber and R. Stora Ed., North Holland, 839-867 (1984). | MR

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

[23] E. Gava, R. Jengo, T. Jayaraman et R. Ramachandran - Multiloop divergences in the closed bosonic string theory, Preprint, Trieste 1985.

[24] P. B. Gilkey - Invariance theory, the heat equation and the Atiyah - Singer index theorem, Publish or Perish, 1984. | MR | Zbl

[25] H. Gillet et Ch. Soulé - Direct images of hermitian holomorphic bundles, Bull. Am. Math. Soc. 15, 209-212 (1986). | MR | Zbl

[26] J. Harer - The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983), 221-239. | MR | Zbl

[27] J. Harris - Recent work on Mg, Proceedings of the International Congress of Mathematicians, Warzawa, North Holland, 1984, Vol. 1, 719-726. | MR | Zbl

[28] S. W. Hawking - Zeta function regularization of path integrals in curved space-time, Comm. Math. Phys. 55, 133-148 (1977). | MR | Zbl

[29] J. I. Igusa - Modular forms and projective invariants, American Journ. of Math. 89, 817-855 (1967). | MR | Zbl

[30] V. G. Knizhnik - Analytic fields on Riemann surfaces, Phys. Lett. B, 180, 247-254 (1986). | MR | Zbl

[31] F. F. Knudsen and D. Mumford - The projectivity of the moduli space of stable curves I : Preliminaries on "det" and "Div", Math. Scand. 39, 19-55 (1976). | MR | Zbl

[32] Yu. I. Manin - Dimensions critiques des théories des cordes et faisceau dualisant sur l'espace des modules des super-courbes, Analyse fonctionnelle et applications 20, n° 3, 88-89 (1986) (en russe). | MR | Zbl

[33] Yu. I. Manin - The partition function of the Polyakov string can be expressed through theta function, Pisma ZETP 43, 161-163 (1986). | MR

[34] Yu. I. Manin - Quantum strings and algebraic curves, Conférence au congrès international des mathématiciens (1986). | MR | Zbl

[35] G. Moore - Modular forms and two-loop string physics, Phys. Lett. B, 176, 369-379 (1986). | MR

[36] G. Moore and P. Nelson - Measure for moduli, Nuclear Physics B 266, 58-74 (1986). | MR

[37] A. Morozov - Explicit formulae for one, two, three and four loop string amplitudes, Preprint ITEP 86-88. | MR

[38] D. Mumford - Abelian quotients of the Teichmüller modular group, Journal d'Analyse Mathématique 18, 227-244 (1967). | MR | Zbl

[39] D. Mumford - Stability of projective varieties, L'Enseignement Mathématique 23, 39-110 (1977). | MR | Zbl

[40] A. Neveu - Dual resonance models and strings in QCD, in Recent advances in field theory and statistical mechanics, Les Houches 1982, J.-B. Zuber and R. Stora Ed., North Holland, 1984, 757-837. | MR

[41] J. Polchinski - Evaluation of the one string path integral, Commun. Math. Phys. 104, 34-47 (1986). | MR | Zbl

[42] A. M. Polyakov - Quantum geometry of bosonic strings, Phys. Lett 103 B, 207-210 (1981). | MR

[43] A. M. Polyakov - Quantum geometry of fermionic strings, Phys. Lett. B, 103, 211-213 (1981). | MR

[44] D. Quillen - Determinants of Cauch - Riemann operators over a Riemann surface, Funk. Anal. i Prilozen 19, 37-41 (1985) [= Funct. Anal. Appl. 19, 31-34 (1986)]. | MR | Zbl

[45] D. Ray and I. M. Singer - R-torsion and the laplacian on riemannian manifolds, Adv. in Math. 7, 145-210 (1971). | MR | Zbl

[46] R. T. Seeley - Complex powers of an elliptic operator, Proc. Symp. Pure Math., AMS, Vol. X, 288-307 (1967). | MR | Zbl

[47] A. Weil - Elliptic functions according to Eisenstein and Kronecker, Springer-Verlag (1976). | MR | Zbl

[48] S. Wolpert - Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces, Preprint, Maryland, 1986. | MR

[49] SÉMINAIRE DE GÉOMÉTRIE ALGÉBRIQUE 6 - Springer Lecture Notes in Mathematics 225 (1971).

[50] Dual theory - Ed. M.Jacob, Physics Reports reprint book series I, North Holland (1974).

[51] VERTEX OPERATORS IN MATHEMATICS AND PHYSICS - Edited by J. Lepowsky, S. Mandelstam and I.M. Singer, MSRI Publications 3, Springer-Verlag (1984). | MR

[52] Superstrings - The first 15 years of superstring theory, Edited by J.H. Schwarz, World Scientific (1985). | MR

[53] M. B. Green, J. H. Schwart and E. Witten - Superstring Theory, Cambridge University Press (1987).

[54] J.-M. Bismut, H. Gillet et Ch. Soulé - Analytic torsion and holomorphic determinant bundles, Prépublication Orsay 87 T 8.