Topological quantum field theories

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Discussion Overview

The discussion revolves around Topological Quantum Field Theories (TQFTs), specifically focusing on Chern-Simons theory and the Crane-Yetter model. Participants explore the existence of other TQFTs and seek introductory explanations and resources related to these theories.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants identify Chern-Simons theory as a 3D TQFT and the Crane-Yetter model as a 4D TQFT.
  • One participant inquires about the existence of other TQFTs beyond Chern-Simons and Crane-Yetter.
  • Another participant provides a brief overview of Chern-Simons theory, noting its gauge invariance, Lorentz invariance, and independence from the background metric.
  • It is mentioned that Ed Witten discovered a relationship between knot theory and Chern-Simons theory.
  • A participant introduces the Turaev-Viro model as another example of a TQFT.
  • Links to introductory papers on Chern-Simons theory are shared for further reading.

Areas of Agreement / Disagreement

Participants generally agree on the identification of Chern-Simons theory and the Crane-Yetter model as TQFTs, but the discussion remains open regarding the existence of other TQFTs and the details of their properties.

Contextual Notes

Some limitations include the lack of detailed explanations about the Turaev-Viro model and the specific implications of the relationship between knot theory and Chern-Simons theory. The discussion does not resolve the inquiry about other TQFTs.

meteor
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Chern-Simons theory is a 3d-TQFT and Crane-Yetter model is a 4d-TQFT
There exist another Topological Quantum Field Theory apart of these two models?
 
Last edited:
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Originally posted by meteor
Chern-Simons theory is a 3d-TQFT and Crane-Yetter model is a 4d-TQFT
There exist another Topological Quantum Field Theory apart of these two models?

Meteor you would be doing me a favor if you could explain a little about Chern-Simons theory and perhaps give some web links---all at very introductory level if possible.
 
Sorry, I'm not an expert on it, so what I'm going to say is probably known to you:
Chern-Simons theory (a.k.a. Chern-Simons gauge theory) is a gauge theory. It's gauge invariant and Lorentz invariant
One of the most important features of Chern-Simons theory is that is independent of the background metric that you choose for the spacetime
In Chern-Simons theory, the field is a connection
Ed Witten discovered in 1989 that exists some relationship between knot theory and Chern-Simons theory
These two papers seem introductory:
http://xxx.lanl.gov/abs/hep-th/9902115
http://xxx.lanl.gov/abs/hep-th/9905057
If this interest to someone, I've discovered that the Turaev-Viro model is another TQFT
 
Last edited:

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