Extension of geodesic algebras to continuous genus
L. Chekhov (Steklov Mathematical Institute, Institute for, Experimental, Theoretical Physics, Moscow, Russia), J.E.Nelson, (Universita`, INFN, Torino, Italy), T. Regge (Politecnico di Torino,, Torino, Italy)
TL;DR
This paper develops a free-field representation for geodesic function algebras on Riemann surfaces with holes, extending to the continuous-genus limit, and demonstrates the natural action of the mapping class group.
Contribution
It introduces a novel free-field representation for geodesic algebras in the continuous-genus limit using Penner--Fock parameterization.
Findings
Representation of geodesic algebras in the continuous-genus limit
Natural action of the mapping class group in the new representation
Extension of algebraic structures to infinite-genus surfaces
Abstract
Using the Penner--Fock parameterization for Teichmuller spaces of Riemann surfaces with holes, we construct the string-like free-field representation of the Poisson and quantum algebras of geodesic functions in the continuous-genus limit. The mapping class group acts naturally in the obtained representation.
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