### Abstract

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.

Original language | English |
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Pages (from-to) | 1027-1063 |

Number of pages | 37 |

Journal | Letters in Mathematical Physics |

Volume | 107 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2017 Jun 1 |

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Letters in Mathematical Physics*,

*107*(6), 1027-1063. https://doi.org/10.1007/s11005-017-0936-0