Non-Perturbative Topological Strings and Conformal Blocks

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Non-Perturbative Topological Strings and Conformal Blocks

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Title: Non-Perturbative Topological Strings and Conformal Blocks
Author: Dijkgraaf, Robbert; Cheng, Miranda Chih-Ning; Vafa, C.

Note: Order does not necessarily reflect citation order of authors.

Citation: Cheng, Miranda, Robbert Dijkgraaf, and Cumrun Vafa. 2011. Non-perturbative topological strings and conformal blocks. Journal of High Energy Physics 2011(9): 022.
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Abstract: 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.
Published Version: doi:10.1007/JHEP09(2011)022
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