occasional meanderings in physics' brave new world
- Name: Kea
- Location: New Zealand
Marni D. Sheppeard
Friday, May 23, 2008
Are the Foaming Loopies secretly doing String Theory at last? The latest paper by Markopoulou et al looks at ribbon graphs in two dimensions and three stranded diagrams in three dimensions. The three strands may be considered as tubes, much as in closed string diagrams. Then the open-closed string duality becomes a duality between 2d simplices and 3d ones. But how can this be? As a Poincare duality one exchanges 2d and 3d objects only in dimension 5, whereas this stringy duality is usually associated with 2-categorical structures. Fortunately, a moduli space perspective solves the mystery. The tube diagram for the tetrahedron is a 4 punctured sphere, the moduli of which is indeed two dimensional. The other two dimensional moduli space is the space of elliptic curves. These two moduli describe duality as envisaged by Grothendieck in his work on ribbon graphs for surfaces.