Non-Perturbative Topological Strings And Conformal Blocks

Details Non-Perturbative Topological Strings And Conformal Blocks Non-Perturbative Topological Strings And Conformal Blocks

2010-10-21

arxiv.org/abs/1010.4573v1

JHEP 1109:022,2011

Physics

High Energy Physics

High Energy Physics - Theory

36 pages

Scientific paper

10.1007/JHEP09(2011)022

We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.

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