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Journal of High Energy Physics

, 2012:19 | Cite as

Quantum geometry of refined topological strings

  • Mina Aganagic
  • Miranda C. N. Cheng
  • Robbert Dijkgraaf
  • Daniel KreflEmail author
  • Cumrun Vafa
Article

Abstract

We consider branes in refined topological strings. We argue that their wavefunctions satisfy a Schrödinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description. Furthermore, in the limit where one of the equivariant rotations approaches zero, the brane partition function satisfies a time-independent Schrödinger equation. We use this observation, as well as the back reaction of the brane on the closed string geometry, to offer an explanation of the connection between integrable systems and \( \mathcal{N}=2 \) gauge systems in four dimensions observed by Nekrasov and Shatashvili.

Keywords

Topological Strings Matrix Models 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Mina Aganagic
    • 1
    • 2
  • Miranda C. N. Cheng
    • 3
    • 4
    • 5
  • Robbert Dijkgraaf
    • 6
  • Daniel Krefl
    • 2
    Email author
  • Cumrun Vafa
    • 4
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyU.S.A.
  2. 2.Center for Theoretical PhysicsUniversity of CaliforniaBerkeleyU.S.A.
  3. 3.Department of MathematicsHarvard UniversityCambridgeU.S.A.
  4. 4.Department of PhysicsHarvard UniversityCambridgeU.S.A.
  5. 5.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.
  6. 6.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands

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