Abstract
We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of “open abelian varieties” which satisfies gluing axioms similar to those of Riemann surfaces, and therefore allows a notion of “conformal field theory” to be defined on this space. We further prove that chiral conformal field theories corresponding to even lattices factor through this moduli space of open abelian varieties.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
T.M. Fiore: Pseudo limits, biadjoints, and pseudo algebras: categorical foundations of conformal field theory, Mem. Amer. Math. Soc. 182 (2006).
T.M. Fiore: On the cobordism and commutative monoid with cancellation approaches to conformal field theory, J. Pure Appl. Algebra 209 (2007) 583–620.
T.M. Fiore, P. Hu, I. Kriz: Laplaza sets, or how to select coherence diagrams for pseudo algebras, to appear in the Advances of Mathematics.
P. Hu, I. Kriz: Conformal field theory and elliptic cohomology, Adv. Math. 189 (2004) 325–412.
P. Hu, I. Kriz: Closed and open conformal field theories and their anomalies, Comm. Math. Phys. 254 (2005) 221–253.
D. Mumford: Abelian varieties, Tata Inst. of Fund. Res. Studies in Math. 5, London 1970.
A. Pressley, G. Segal: Loop groups, Oxford Math. Monographs, Oxford University Press 1986.
B. Riemann: Theorie der Abelschen Functionen, J. Reine und Angew. Mathematik 54 (1857) 101–155.
G. Segal: The definition of conformal field theory, Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser. 308, Cambridge University Press, 2004, 421–577.
G. Segal: Unitary representations of some infinite-dimensional groups, Comm. Math. Phys. 80 (1981). 301–342.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH
About this chapter
Cite this chapter
Fiore, T.M., Kriz, I. (2010). What is the Jacobian of a Riemann Surface with Boundary?. In: Abbaspour, H., Marcolli, M., Tradler, T. (eds) Deformation Spaces. Vieweg+Teubner. https://doi.org/10.1007/978-3-8348-9680-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-8348-9680-3_2
Publisher Name: Vieweg+Teubner
Print ISBN: 978-3-8348-1271-1
Online ISBN: 978-3-8348-9680-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)