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


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.


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

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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.