# Linking loops in ABJM and refined theory

Taro Kimura

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

Abstract: We consider the link average of the half-BPS Wilson loop operators in N=6$$\mathcal{N}=6$$ superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the two- and three-link averages with an operator formalism inspired by a three-dimensional topological field theory. We obtain a factorization of the link average, and the Verlinde formula in a sector of supergroup representations. We also propose a refined version of ABJM theory, and compute some refined link averages.

Original language English 30 Journal of High Energy Physics 2015 7 https://doi.org/10.1007/JHEP07(2015)030 Published - 2015 Jul 22

operators
matrices
factorization
sectors
formalism

### Keywords

• Chern-Simons Theories
• Matrix Models

### ASJC Scopus subject areas

• Nuclear and High Energy Physics

### Cite this

Linking loops in ABJM and refined theory. / Kimura, Taro.

In: Journal of High Energy Physics, Vol. 2015, No. 7, 30, 22.07.2015.

Research output: Contribution to journalArticle

Kimura, Taro. / Linking loops in ABJM and refined theory. In: Journal of High Energy Physics. 2015 ; Vol. 2015, No. 7.
@article{c07b394a5a684f23aae196c20862d5fc,
title = "Linking loops in ABJM and refined theory",
abstract = "Abstract: We consider the link average of the half-BPS Wilson loop operators in N=6$$\mathcal{N}=6$$ superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the two- and three-link averages with an operator formalism inspired by a three-dimensional topological field theory. We obtain a factorization of the link average, and the Verlinde formula in a sector of supergroup representations. We also propose a refined version of ABJM theory, and compute some refined link averages.",
keywords = "Chern-Simons Theories, Matrix Models",
author = "Taro Kimura",
year = "2015",
month = "7",
day = "22",
doi = "10.1007/JHEP07(2015)030",
language = "English",
volume = "2015",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",
number = "7",

}

TY - JOUR

T1 - Linking loops in ABJM and refined theory

AU - Kimura, Taro

PY - 2015/7/22

Y1 - 2015/7/22

N2 - Abstract: We consider the link average of the half-BPS Wilson loop operators in N=6$$\mathcal{N}=6$$ superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the two- and three-link averages with an operator formalism inspired by a three-dimensional topological field theory. We obtain a factorization of the link average, and the Verlinde formula in a sector of supergroup representations. We also propose a refined version of ABJM theory, and compute some refined link averages.

AB - Abstract: We consider the link average of the half-BPS Wilson loop operators in N=6$$\mathcal{N}=6$$ superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the two- and three-link averages with an operator formalism inspired by a three-dimensional topological field theory. We obtain a factorization of the link average, and the Verlinde formula in a sector of supergroup representations. We also propose a refined version of ABJM theory, and compute some refined link averages.

KW - Chern-Simons Theories

KW - Matrix Models

UR - http://www.scopus.com/inward/record.url?scp=84937566334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937566334&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2015)030

DO - 10.1007/JHEP07(2015)030

M3 - Article

AN - SCOPUS:84937566334

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 30

ER -