Abstract
The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two-and three-point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b−c systems. The defining cocycle for this central extension deforms to the well-known Virasoro cocycle for certain kinds of degenerations of the torus.
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References
BonoraL., MatoneM., and RinaldiM., Relations between representations of KN and Virasoro algebras, Phys. Lett. B 216, 313 (1989).
Deck, Th., Stringtheorie und Krichever-Novikov-Algebren auf Tori, Diplomarbeit Universität Karlsruhe, 1990.
DeckTh., Deformations from Virasoro to Krichever-Novikov algebras, Phys. Lett. B 251, 535–540 (1990).
DickR., Krichever-Novikov-like bases on punctured Riemann surfaces, Lett. Math. Phys. 18, 255 (1989).
Dick, R., Global expansions of holomorphic differentials on punctured Riemann surfaces, desy preprint 89-160 (1989).
Dick, R., Chiral fields on Riemann surfaces and string vertices, Dissertation Universität Hamburg, Germany, 1990.
Dick, R., Topological aspects of Chiral fields in two dimensions and superstring vertices, Fortschr. Phys.
Dick, R., The quadruplet of central charges on the sphere, in G. Domokos and S. Kövesi-Domokos (eds), Proc. 14th Johns Hopkins Workshop on Current Problems in Particle Theory (1990).
GuoH-y., NaJ-s., ShenJ-m., WangS-k., and YuQ-h., The algebras of meromorphic vector fields ... Comm. Theor. Phys. 12, 349–354 (1989).
HurwitzA. and CourantR., Allgemeine Funktionentheorie und elliptische Funktionen, Springer, Berlin, 1964.
KricheverI. M. and NovikovS. P., Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons, Funktional anal. i. Prilozhen. 21(2), 46 (1987); Virasoro type algebras, Riemann surfaces and strings in Minkowski space, Funktional Anal. i. Prilozhen. 21(4), 47 (1987).
RauchH. E. and LebowitzA., Elliptic Functions, Theta Functions and Riemann Surfaces, Williams & Wilkins, Baltimore, 1973.
Ruffing, A., Prozessinduzierte symmetrische Basiskonstruktion ..., Diplomarbeit Universität Karlsruhe, 1991.
SchlichenmaierM., An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces, Lecture Notes in Physics 322, Springer, New York, 1989.
SchlichenmaierM., Krichever-Novikov algebras for more than two points, Lett. Math. Phys. 19, 151–165 (1990).
SchlichenmaierM., Krichever-Novikov algebras for more than two points: explicit generators, Lett. Math. Phys. 19, 327–336 (1990).
SchlichenmaierM., Central extensions and semi-infinite wedge representations of Krichever-Novikov algebras for more than two points, Lett. Math. Phys. 20, 33–46 (1990).
Schlichenmaier, M., Verallgemeinerte Krichever-Novikov Algebren und deren darstellungen, Dissertation Universität Mannheim, Gremany (1990).
Schlichenmaier, M., Degenerations of generalized Krichever-Novikov algebras, Mannheimer Manuskripte 137 (1992).
BremnerM. R., On a Lie algebra of vector fields on a complex torus, J. Math. Phys. 31, 2033–2034 (1990).
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Ruffing, A., Deck, T. & Schlichenmaier, M. String branchings on complex tori and algebraic representations of generalized Krichever-Novikov algebras. Lett Math Phys 26, 23–32 (1992). https://doi.org/10.1007/BF00420515
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DOI: https://doi.org/10.1007/BF00420515