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

Bertrand Eynard, Taro Kimura

研究成果: Article査読

4 被引用数 (Scopus)


We study U (N| M) 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 U (N| M) character expectation values in terms of U (1 | 1) averages for a particular type of character representations. This means that the U (1 | 1) character expectation value is a building block for the U (N| M) averages and also, by an appropriate limit, for the U (N) 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.

ジャーナルLetters in Mathematical Physics
出版ステータスPublished - 2017 6月 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学


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