Abstract
Witten (Two dimensional gravity and intersection theory on moduli space, surveys in differential geometry 1, 243–310, 1991, [134]) conjectured that a generating function of the intersection numbers of the moduli space of curves on a Riemann surface with marked points, is a solution of the KdV hierarchy. Kontsevich (Commun Math Phys 147:1–23, 1992, [89]) has proved this conjecture with the use of an Airy matrix model. In addition it has been realized that matrix models of this type are examples of an exact closed/open strings duality (Gaiotto and Rastelli, JHEP 07:053, 2005, [63]).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 The Author(s)
About this chapter
Cite this chapter
Brézin, E., Hikami, S. (2016). Intersection Numbers of Curves. In: Random Matrix Theory with an External Source. SpringerBriefs in Mathematical Physics, vol 19. Springer, Singapore. https://doi.org/10.1007/978-981-10-3316-2_6
Download citation
DOI: https://doi.org/10.1007/978-981-10-3316-2_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3315-5
Online ISBN: 978-981-10-3316-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)