The geometry of the light-cone cell decomposition of moduli space

Journal Article · Sun Nov 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4934365· OSTI ID:22479554

Garner, David; Ramgoolam, Sanjaye ^[1]

---

1. Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)

The moduli space of Riemann surfaces with at least two punctures can be decomposed into a cell complex by using a particular family of ribbon graphs called Nakamura graphs. We distinguish the moduli space with all punctures labelled from that with a single labelled puncture. In both cases, we describe a cell decomposition where the cells are parametrised by graphs or equivalence classes of finite sequences (tuples) of permutations. Each cell is a convex polytope defined by a system of linear equations and inequalities relating light-cone string parameters, quotiented by the automorphism group of the graph. We give explicit examples of the cell decomposition at low genus with few punctures.

• OSTI ID: 22479554
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIAGRAMS
EQUATIONS
GEOMETRY
GRAPH THEORY
LIGHT CONE
RIEMANN SHEET