×

zbMATH — the first resource for mathematics

Critical dimensions of the string theories and the dualizing sheaf on the moduli space of (super) curves. (English. Russian original) Zbl 0639.14015
Funct. Anal. Appl. 20, 244-246 (1986); translation from Funkts. Anal. Prilozh. 20, No. 3, 88-89 (1986).
The observation in this note, that the critical dimensions 26 and 10 which occur in the theory of strings and superstrings can be observed from the results of D. Mumford [Enseign. Math., II. Ser. 23, 39-110 (1977; Zbl 0363.14003)] on the moduli space of stable curves, has been of fundamental importance in the by now highly developed techniques in string theory. The author suggests also in this paper that the moduli space for \(g\to \infty\) should play a role for the Virasoro algebra analogous to that of the flag manifold for a simple Lie algebra.
Reviewer: N.J.Hitchin

MSC:
14H15 Families, moduli of curves (analytic)
81T08 Constructive quantum field theory
58D30 Applications of manifolds of mappings to the sciences
14H10 Families, moduli of curves (algebraic)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. H. Schwarz, Phys. Rep.,89, 223-305 (1982). · Zbl 0578.22027
[2] D. Gross, J. Harvey, E. Martinec, and R. Rohm, Heterotic String Theory, Preprint, Princeton (1985).
[3] A. M. Polyakov, Phys. Lett.,103B, 207-210 (1981).
[4] O. Alvarez, Nucl. Phys.,216, 125-184 (1983).
[5] D. Mumford, Ens. Math.,24, 39-110 (1977).
[6] B. L. Feigin, Usp. Mat. Nauk,39, No. 2, 195-196 (1984).
[7] T. Shiota, Characterization of Jacobian Varieties in Terms of Soliton Equations, Preprint, Harvard (1984). · Zbl 0621.35097
[8] Yu. I. Manin and A. O. Radul, Commun. Math. Phys.,98, 65-77 (1985). · Zbl 0607.35075
[9] I. B. Penkov, Inv. Math.,71, No. 3, 501-512 (1983). · Zbl 0528.32012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.