Abstract
New formulation of bosonization is given so that it is defined over the ring Z of integers. The charge zero sector of the new boson Fock space is the completion of the coordinate ring of the universal Witt scheme. By using new bosonization, conformal field theory of free fermions over Z is given.
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Arbarello, E., De Concini, C., Kac, V., Procesi, C.: Moduli spaces of curves and representation theory. Commun. Math. Phys.117, 1–36 (1988)
Alvarez-Gaumé, L., Bost, J.-B., Moore, G., Nelson, P., Vafa, C.: Bosonization of higher genus Riemann surfaces. Commun. Math. Phys.112, 503–552 (1987)
Alvarez-Gaumé, L., Gomez, C., Reina, C.: Loop groups, grassmannians and string theory. Phys. Lett.190 B, 55–62 (1987)
Bost, J. B.: Fibrés déterminants régularisés et mesures sur les espaces de modules des courbes complex. Sém. Bourbaki, 1986–7, Exposé 676
Belavin, A. A., Knizhnik, V. G.: Complex geometry and theory of quantum strings. Sov. Phys. JETP64, 214–228 (1986)
Beilinson, A. A., Manin, Yu. I.: The Mumford form and the Polyakov measure in string theory. Commun. Math. Phys.107, 359–376 (1986)
Beilinson, A. A., Manin, Yu. I., Shechtman, V. V.: Localization of the Virasoro and Neveu-Schwarz algebra. Moscow, preprint (1986)
Beilinson, A. A., Shechtman, V. V.: Determinant bundles and Virasoro algebras. Commun. Math. Phys.118, 651–701 (1988)
Date, E., Jimbo, M., Kashiwara, M. and Miwa, T.: Transformation groups for soliton equations. In: Proc. of RIMS Symp. on Non-linear Integrable Systems—Classical theory and quantum theory. Kyoto, Japan. Jimbo, M., Miwa, T., (eds.), pp. 39–119. Singapore: World Scientific 1983
Eguchi, T., Ooguri, H.: Chiral bosonization on a Riemann surface. Phys. Letter187B, 127–134 (1987)
Freund, P. G. O., Olson, M.: Non-archimedian strings. Phys. Lett.199B, 1987
Freund, P. G. O., Witten, E.: Adelic string amplitudes, Phys. Lett.199B, 191–194, 1987
Friedan, D.: The modular geometry of string theory and conformal field theory. Preprint, 1987
Friedan, D., Shenker, S. H.: The analytic geometry of conformal field theory. Nucl. Phys.281B, 509–545 (1987)
Hartshorne, R.: Algebraic geometry, graduate texts in mathematics, vol. 52. Berlin, Heidelberg, Yew York: Springer 1977
Ishibashi, N., Matsuo, Y., Ooguri, H.: Soliton equations and free fermions on Riemann surfaces. Mod. Phys. Lett.A2, 119–131 (1987)
Kawamoto, N., Namikawa, Y., Tsuchiya, A., Yamada, Y.: Geometric realization of conformal field theory on Riemann surfaces. Commun. Math. Phys.116, 247–308 (1988)
Manin, Yu. I.: New dimensions in geometry. Lecture Notes in Mathematics, vol.1111, pp. 59–101. Berlin, Heidelberg, New York: Springer 1985
Mann, Yu. I.: Reflections on arithmetical physics. Preprint 1987
Mumford, D.: Lectures on curves on an algebraic surface. Ann. Math. Studies 59, Princeton, New Jersey: Princeton Univ. Press 1966
Oort, F., Steenbrink, J.: The local Torelli problem for algebraic curves. In: Algebraic geometry, Angers 1979, 157–204, Sijthoff & Noordhoff 1980
Sato, M., Noumi, M.: Soliton equation and universal Grassmann manifold. Sophia Univ. Kôkyuroku in Math. vol.18 (in Japanese) 1984
Sato, M., Sato, Y.: Soliton equations as dynamical systems on infinite dimensional grassmann manifold. In: Proc. U.S.-Japan Seminar, Tokyo, 1982. Nonlinear partial differential equations in applied science. Fujita, H., Lax, P. D., Strang, G., (eds.), pp. 259–271. Kinikuniya and North-Holland 1982
Shafarevich, I. R.: Basic algebraic geometry. Berlin, Heidelberg, New York: Springer 1974
Smit, D.-J.: String theory and algebraic geometry of moduli spaces. Commun. Math. Phys.114, 645–685 (1988)
Ueno, K.: Bosonic strings and arithmetic surfaces. Kyoto Univ. preprint, 1986
Volovich, I. V.: Number theory as the ultimate physical theory, preprint, CERN-TH.4781/87
Verlinde, E., Verlinde, H.: Chiral bosonization, determinants and the string partition function. Nucl. Phys.B288, 357–396 (1987)
Witten, E.: Quantum field theory, Grassmannians, and algebraic curves. Commun. Math. Phys.113, 529–600 (1988)
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Communicated by H. Araki
Dedicated to Professor M. Sato on his sixtieth birthday
Partially supported by Max-Planck-Institut für Mathematik
Partially supported by Max-Planck-Institut für Mathematik
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Katsura, T., Shimizu, Y. & Ueno, K. New bosonization and conformal field theory over Z. Commun.Math. Phys. 121, 603–627 (1989). https://doi.org/10.1007/BF01218158
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DOI: https://doi.org/10.1007/BF01218158