Toward U(N|M) knot invariant from ABJM theory

Bertrand Eynard, Taro Kimura

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1 Citation (Scopus)


We study (Formula presented.) character expectation value with the supermatrix Chern–Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half-BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives (Formula presented.) character expectation values in terms of (Formula presented.) averages for a particular type of character representations. This means that the (Formula presented.) character expectation value is a building block for the (Formula presented.) averages and also, by an appropriate limit, for the (Formula presented.) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern–Simons matrix model. We obtain the Rosso–Jones-type formula and the spectral curve for this case.

Original languageEnglish
Pages (from-to)1-37
Number of pages37
JournalLetters in Mathematical Physics
Publication statusAccepted/In press - 2017 Feb 1



  • ABJM theory
  • Chern–Simons theory
  • Knot invariant
  • Matrix model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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