Journal of High Energy Physics

, 2014:168 | Cite as

Non-perturbative effects and the refined topological string

  • Yasuyuki Hatsuda
  • Marcos MariñoEmail author
  • Sanefumi Moriyama
  • Kazumi Okuyama
Open Access


The partition function of ABJM theory on the three-sphere has nonperturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local ℙ1 × ℙ1, in the NekrasovShatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.


AdS-CFT Correspondence Topological Strings M-Theory 


Open Access

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Yasuyuki Hatsuda
    • 1
    • 2
  • Marcos Mariño
    • 3
    Email author
  • Sanefumi Moriyama
    • 4
  • Kazumi Okuyama
    • 5
  1. 1.DESY Theory Group, DESY HamburgHamburgGermany
  2. 2.Department of PhysicsTokyo Institute of TechnologyTokyoJapan
  3. 3.Département de Physique Théorique et section de MathématiquesUniversité de GenèveGenèveSwitzerland
  4. 4.Kobayashi Maskawa Institute and Graduate School of MathematicsNagoya UniversityNagoyaJapan
  5. 5.Department of PhysicsShinshu UniversityMatsumotoJapan

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