### Abstract

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 language | English |
---|---|

Pages (from-to) | 1-37 |

Number of pages | 37 |

Journal | Letters in Mathematical Physics |

DOIs | |

Publication status | Accepted/In press - 2017 Feb 1 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*, 1-37. https://doi.org/10.1007/s11005-017-0936-0

**Toward U(N|M) knot invariant from ABJM theory.** / Eynard, Bertrand; Kimura, Taro.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, pp. 1-37. https://doi.org/10.1007/s11005-017-0936-0

}

TY - JOUR

T1 - Toward U(N|M) knot invariant from ABJM theory

AU - Eynard, Bertrand

AU - Kimura, Taro

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - ABJM theory

KW - Chern–Simons theory

KW - Knot invariant

KW - Matrix model

UR - http://www.scopus.com/inward/record.url?scp=85011265970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011265970&partnerID=8YFLogxK

U2 - 10.1007/s11005-017-0936-0

DO - 10.1007/s11005-017-0936-0

M3 - Article

AN - SCOPUS:85011265970

SP - 1

EP - 37

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -