All Questions
24
questions
0
votes
1
answer
81
views
Gauge fixing in derivation of fractional QHE action
I'll copy the text from a relevant question:
This follows the discussion in Altland and Simons Condensed Matter
Field Theory -- section 9.5 on deriving the Chern-Simons action for
FQHE.
Starting with ...
- 157
1
vote
0
answers
142
views
Chern-Simons Realization of Dijkgraaf-Witten Theory
There is a realization of $Z_N$ Chern-Simons theory (Dijkgraaf-Witten theory) using an instance of $U(1) \times U(1)$ Chern-Simons theory. As explained on page 38 of https://arxiv.org/abs/2007.05915 , ...
- 1,171
5
votes
1
answer
606
views
Propagator of four-dimensional Chern-Simons theory
In https://arxiv.org/abs/1903.03601, on page 13, the propagator of 4d Chern-Simons theory is computed, in the gauge $D^iA_i=0$, where $D^i = (\partial_x,\partial_y,4\partial_z)$.
The gauge-fixed ...
- 1,171
4
votes
1
answer
155
views
Knots in 3d pure gravity
Three-dimensional pure gravity on $\mathrm{AdS}_3$ can be described as a Chern-Simons theory with gauge group $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$,with action
$$ S[A,\bar{A}] = \...
- 4,654
3
votes
0
answers
58
views
Is the "Push-Down" Quantization of Chern-Simons Theory part of a more general approach to Quantization?
I've recently started reading Axelrod, Della Pietra and Witten's original paper about the quantization of Chern-Simons theory. I'd like to know if the "push-down" quantization strategy they ...
1
vote
0
answers
116
views
Are central charges equal or similar to irreducible spinor representations?
First of, if any of the following below does not make sense, please feel free to leave a comment =)
Central charges in Chern Simons in in the Virasoro conformal blocks play an important role for ...
- 47
5
votes
1
answer
430
views
How do $\theta$-terms not violate gauge invariance?
In the context of QCD (and more generally, any quantum gauge theory in even dimensions), the $\theta$-term is
$$
\frac{\theta}{8\pi^2}\langle F_A\wedge F_A\rangle = \frac{\theta}{32\pi^2}\langle F_A^{\...
- 338
5
votes
1
answer
315
views
Normalization of the Chern-Simons action in the Dijkgraaf-Witten paper
I am trying to understand the seminal paper "Topological gauge theories and group cohomology" by Dijkgraaf and Witten. They consider an oriented three-manifold $M$, compact Lie group $G$ and a $G$-...
- 2,191
2
votes
1
answer
268
views
Induced "ungauged" Chern-Simons terms from a massive Dirac fermion
It is a well-known fact that a massive Dirac fermion minimally coupled to a gauge field $A_\mu$ induces a Chern-Simons term when integrating out the fermion:
\begin{align}
i\bar{\psi}\gamma^\mu(\...
- 2,949
4
votes
1
answer
235
views
Chern-Simons theory on a plane/sphere with a single charge insertion
Consider the pure Chern-Simons theory on the plane $\mathbb{R}^2$ with a single charge insertion in some representation $\rho$ of the group $G$. What does the Hilbert space look like? Is it null or ...
- 16.2k
3
votes
0
answers
218
views
Gauge and global symmetries in Chern-Simons/WZW correspondence
I am trying to understand how bulk gauge symmetry in 3d Chern-Simons theory becomes a global symmetry in the boundary 2d WZW theory. In particular, I am trying to understand the papers by Elitzur et ...
- 1,171
4
votes
1
answer
477
views
Path integral measure in Chern-Simons/WZW correspondence
The relationship between 3d Chern-Simons theory on the product of the disk and the real line ($D\times \mathbb{R}$) and the chiral WZW model on $S^1\times \mathbb{R}$ was shown in Elitzur et al Nucl....
- 1,171
5
votes
0
answers
205
views
Is it possible to couple an odd number of Dirac fermions, at finite density, to a massless gauge field in 2+1d?
In a beautiful paper by A. N. Redlich (PRL $\bf{52}$, 18 (1984)) on the parity anomaly, the author indicates that an odd number of Dirac fermions can never be coupled to a massless gauge field in 2+1d ...
- 51
13
votes
1
answer
772
views
Faddeev-Popov Determinant of Chern-Simons Theory
I am asking this question in order to figure out the expression of the Faddeev-Popov determinant given by Edward Witten is his paper "Quantum Field Theory and Jones Polynomial".
Starting from the ...
- 2,923
7
votes
1
answer
712
views
The Hilbert space of Chern-Simons on a torus, part one$.$
There is a key result in 2+1 dimensional Chern-Simons theory, which was first discussed in ref.1.: the Hilbert space of the theory, when quantised on $T^2\times\mathbb R$, is isomorphic to
$$
\frac{\...
