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Instanton bound states in ABJM theory

  • Yasuyuki HatsudaEmail author
  • Sanefumi Moriyama
  • Kazumi Okuyama
Open Access
Article

Abstract

The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.

Keywords

Matrix Models Chern-Simons Theories Nonperturbative Effects M-Theory 

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Copyright information

© SISSA 2013

Authors and Affiliations

  • Yasuyuki Hatsuda
    • 1
    • 2
    Email author
  • Sanefumi Moriyama
    • 3
  • Kazumi Okuyama
    • 4
  1. 1.DESY Theory Group, DESY HamburgHamburgGermany
  2. 2.Department of PhysicsTokyo Institute of TechnologyTokyoJapan
  3. 3.Kobayashi Maskawa Institute & Graduate School of MathematicsNagoya UniversityNagoyaJapan
  4. 4.Department of PhysicsShinshu UniversityMatsumotoJapan

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