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ABJ fractional brane from ABJM Wilson loop

  • Sho Matsumoto
  • Sanefumi MoriyamaEmail author
Open Access
Article

Abstract

We present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop operator in the corresponding ABJM matrix model. Using this formalism, we study the phase part of the ABJ partition function numerically and find a simple expression for it. We further compute a few exact values of the partition function at some coupling constants. Fitting these exact values against the expected form of the grand potential, we can determine the grand potential with exact coefficients. The results at various coupling constants enable us to conjecture an explicit form of the grand potential for general coupling constants. The part of the conjectured grand potential from the perturbative sum, worldsheet instantons and bound states is regarded as a natural generalization of that in the ABJM matrix model, though the membrane instanton part contains a new contribution.

Keywords

Matrix Models Wilson ’t Hooft and Polyakov loops Nonperturbative Effects M-Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  2. 2.Kobayashi Maskawa InstituteNagoya UniversityNagoyaJapan
  3. 3.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan

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