Gauge theories, vertex models, and quantum groups

Edward Witten

doi:10.1016/0550-3213(90)90115-T

Gauge theories, vertex models, and quantum groups

Edward Witten

Research output: Contribution to journal › Article › peer-review

213 Scopus citations

Abstract

It is known that the Jones polynomial of knot theory, and its generalizations, are closely related to the integrable "vertex models" of two-dimensional statistical mechanics, and to quantum groups. In this paper, an attempt is made to show on a priori grounds, starting only from general covariance of three-dimensional Chern-Simons gauge theory and two-dimensional "duality", why this must be so.

Original language	English (US)
Pages (from-to)	285-346
Number of pages	62
Journal	Nuclear Physics, Section B
Volume	330
Issue number	2-3
DOIs	https://doi.org/10.1016/0550-3213(90)90115-T
State	Published - Jan 29 1990
Externally published	Yes

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

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10.1016/0550-3213(90)90115-T

Cite this

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title = "Gauge theories, vertex models, and quantum groups",

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author = "Edward Witten",

note = "Funding Information: supported in part by NSF Grant 86-20266 and NSF Waterman Grant 88-17521.",

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Y1 - 1990/1/29

N2 - It is known that the Jones polynomial of knot theory, and its generalizations, are closely related to the integrable "vertex models" of two-dimensional statistical mechanics, and to quantum groups. In this paper, an attempt is made to show on a priori grounds, starting only from general covariance of three-dimensional Chern-Simons gauge theory and two-dimensional "duality", why this must be so.

AB - It is known that the Jones polynomial of knot theory, and its generalizations, are closely related to the integrable "vertex models" of two-dimensional statistical mechanics, and to quantum groups. In this paper, an attempt is made to show on a priori grounds, starting only from general covariance of three-dimensional Chern-Simons gauge theory and two-dimensional "duality", why this must be so.

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U2 - 10.1016/0550-3213(90)90115-T

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ER -

Gauge theories, vertex models, and quantum groups

Abstract

All Science Journal Classification (ASJC) codes

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