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CHERN–SIMONS THEORY AND KNOT INVARIANTS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents various aspects of Chern-Simons theory. In a groundbreaking paper, Witten (1989) showed that Chern-Simons gauge theory, which is a quantum field theory in three dimensions, ... More


STRING THEORY AND GAUGE THEORY

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines the relationship between gauge theories and topological strings. A precise correspondence between string theory and gauge theory was formulated by 't Hooft (1974), who used as a ... More


Chern-Simons Theory, Matrix Models, and Topological Strings

Marcos Mariño

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string ... More


STRING FIELD THEORY AND GAUGE THEORIES

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter shows that both Chern-Simons gauge theories and matrix models with polynomial potentials can be realized as open string theories. To show that Chern-Simons theory and matrix models with ... More


APPLICATIONS OF THE TOPOLOGICAL STRING/GAUGE THEORY CORRESPONDENCE

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter considers two applications of the topological string/gauge theory correspondence. The first application is to Chern-Simons knot and link invariants, and the second application is to ... More


Theory of Quantum Hall States

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.07
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Electrons on the interface of two semiconductors can form a new state of matter — fractional quantum Hall (FQH) state — under strong magnetic fields. FQH states cannot be described by Landau symmetry ... More


An introduction to topological phases of electrons

Joel E. Moore

in Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School: Volume 103, August 2014

Published in print:
2017
Published Online:
March 2017
ISBN:
9780198785781
eISBN:
9780191827600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198785781.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

These lecture notes seek to present a coherent picture of some key aspects of topological insulators and the quantum Hall effect. Rather than aiming for completeness or historical accuracy, the goal ... More


THE TOPOLOGICAL VERTEX

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0009
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter explains the cut-and-paste approach to toric Calabi-Yau manifolds developed previously with the large-N duality relating Chern-Simons theory and topological strings, to find a building ... More


Topological field theory

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0031
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Topological field theories are discussed and this chapter provides some concrete examples of applications of these ideas by discussing anyons, fractional statistics and Chern–Simons theories.


Two Lectures on the Jones Polynomial and Khovanov Homology

Edward Witten

in Lectures on Geometry

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198784913
eISBN:
9780191827150
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198784913.003.0001
Subject:
Mathematics, Geometry / Topology

In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret ... More


The fractional quantum Hall fluid

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0046
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The fractional quantum Hall effect is introduced in this chapter and it explains how quasiparticles carrying fractional charge emerge in this theory.


Topological and Quantum order—beyond Landau’s Theories

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.08
Subject:
Physics, Theoretical, Computational, and Statistical Physics

According to the principle of emergence, the properties of material are mainly determined by how the atoms are organized in the material. Such organization is formally called order. The vast range of ... More


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