# Questions tagged [chern-simons-theory]

Chern-Simons theory is an example of a topological quantum field theory. Its describes the field dynamics through the so-called Chern-Simons-form, hence its name.

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### Varying the Chern-Simons action

Summary/TL;DR I want a detailed calculation of the derivation of classical equations of motion from the Chern-Simons action using differential forms, using variational derivatives. I mentioned "...
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### Feynman rule from dynamical Chern-Simons

Consider the following action that $$S = \int d^4x\sqrt{-g}\left(-\frac{1}{2}(\partial\phi)^2 + V(\phi) + \frac{2R}{\kappa^2} - \frac{\phi}{4f}{}^*RR\right)$$ where \...
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### Chern-Simons (K matrix) theory and ${\rm Spin}^{\mathbb C}$ connections

If I understand correctly (e.g. from this paper), an Abelian bosonic Chern-Simons theory defined on $T^2\times \mathbb R$ is specified by a $K$ matrix via e.g. $S \sim \int_M K_{IJ}A^I \wedge dA^J$. ...
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### How is classical Chern-Simons theory topological?

Note: I am using "global" and "topological" somewhat interchangable. This seems to be the case in texts and papers, but please point out if this is inappropriate. Classical Chern-...
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### Class of on-shell and gauge equivalent potentials in Chern-Simons theory

Let $(P, M, \pi, G)$ be a principal bundle with three dimensional manifold $M$ and compact, connected, simply-connected, and simple structure group $G$. We define a Lie algebra valued connection $1$ ...
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### What is the meaning of the statistical gauge field in the fractional quantum Hall effect

I'm a grad student studying the fractional quantum Hall effect. To get started, I read chapter 9.5.1 of A. Altland and B. Simons' Condensed Matter Field Theory. They use the composite fermion (CF) ...
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### Normalization in the Abelian Chern-Simons action

In all the places I looked (such as chapter 5 in the lecture notes of David tong (http://www.damtp.cam.ac.uk/user/tong/qhe.html) and E. Witten (https://arxiv.org/abs/1510.07698)) the action for the ...
1 vote
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### Non-Abelian Chern-Simons Theory References

I am studying Chern-Simons theories and am fairly familiar with the usual Abelian $U(1)$ Chern-Simons theory. I am now looking to extend my knowledge to non-Abelian Chern-Simons and am having a hard ...
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### Does the total Zak phase always sum to zero?

In 2D, the sum of the Chern numbers over all bands is zero. However, this result relies on the ability to define a Berry curvature, which is only possible in $d \geq 2$ dimensions. In 1D it is ...
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