Journal of High Energy Physics

, 2011:22

Non-perturbative topological strings and conformal blocks

  • Miranda C. N. Cheng
  • Robbert Dijkgraaf
  • Cumrun Vafa
Open AccessArticle

DOI: 10.1007/JHEP09(2011)022

Cite this article as:
Cheng, M.C.N., Dijkgraaf, R. & Vafa, C. J. High Energ. Phys. (2011) 2011: 22. doi:10.1007/JHEP09(2011)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.

Keywords

Topological StringsMatrix ModelsDuality in Gauge Field Theories
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© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Miranda C. N. Cheng
    • 1
    • 2
  • Robbert Dijkgraaf
    • 3
  • Cumrun Vafa
    • 4
  1. 1.Department of MathematicsHarvard UniversityCambridgeU.S.A.
  2. 2.Department of PhysicsHarvard UniversityCambridgeU.S.A.
  3. 3.Institute for Theoretical Physics & KdV Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.Center for Theoretical PhysicsMassachusetts Institute of TechologyCambridgeU.S.A.