All Questions
Tagged with duality field-theory
16
questions
2
votes
0
answers
37
views
Superfluid-Maxwell duality and confinement in 3D
I learned in a class I took that there is a duality between a $D=3$ superfluid and $D=3$ Maxwell theory ($D$ being the dimension of spacetime). In the Euclidean formulation, the action of the ...
- 3,710
1
vote
2
answers
153
views
Is it possible to elevate the electric-magnetic duality discrete symmetry to a continuous one?
I'm familiar with Electric-Magnetic duality, where in the absence of source fields one can exchange the $F_{\mu \nu}$ field with the dual field: $\tilde{F}_{\mu \nu}={\epsilon}_{\mu \nu \alpha \beta}
...
- 1,268
2
votes
0
answers
67
views
How to identify the dyon being condensated at the ${\cal N}=2$ SUSY $u$-plane?
For the $u$-plane monodromy at $u=u_0$
$$\mathcal{M}^{p,q}=\begin{pmatrix}
1+pq & p^2 \\
-q^2 & 1-pq \\
\end{pmatrix}$$
the statement is that dyons with electric and magnetic charges $(p,q)$ ...
- 169
1
vote
2
answers
339
views
Some questions about the compact boson in David Tong's notes on Gauge Theory
The notes can be found at http://www.damtp.cam.ac.uk/user/tong/gaugetheory.html.
In Sec. 7.5.1, T-Duality, around Eq. 7.51, it says that the Bianchi identity $\partial_\mu(\epsilon^{\mu\nu}\partial_\...
- 117
1
vote
0
answers
70
views
Explicitly determining the propagator for the dual field
So I have a question which has been on my mind for some time but I never got around to asking: how can I calculate the propagator for a dual field?
Let me go into some more detail. Starting off with ...
- 413
6
votes
1
answer
287
views
Why is the electromagnetic duality an S-duality?
One of the examples that Wikipedia gives of S-duality is the EM duality. Namely that
$$
\begin{align}
\mathbf{E} &\rightarrow\mathbf{B} \\
\mathbf{B} &\rightarrow -\frac{1}{c^2}\mathbf{E} \...
- 1,544
2
votes
0
answers
122
views
What's the symmetry group $SU(N)/Z_N$?
I'm trying to understand David Tong's notes, specifically the discussion around page 92 where he's arguing that a different symmetry group may the group of QCD, namely $G'=SU(N)/Z_N$ instead of $G=SU(...
- 43
5
votes
1
answer
208
views
The planar limit, self-duality and their relation to two dimensions
In the lecture notes by Beisert on integrability, it is stated that integrability is a property mainly in two-dimensional field theories, with some higher-dimensional examples. As higher-dimensional ...
user172341
2
votes
1
answer
280
views
Electromagnetic duality interacting with a complex scalar field
My question refers to example theory introduced in the book "Supergravity" from D.Z.Freedman & A. van Proeyen p.80. Its Lagrangian is given by
$${\cal L}(Z,F) =-\frac{1}{4}(Im Z)F_{\mu\...
- 9,778
4
votes
0
answers
243
views
Constructing a Hubbard-Stratonovich Transform that goes from a theory of Electrostatics to a theory like Magnetostatics
I'm talking about a completely classical theory.
Suppose I start with
$$H = \int(\nabla \phi)^2 $$
I am talking about calculation of the partition function here
$$Z = \int D[\phi] e^{(-\beta\int(\...
4
votes
1
answer
804
views
How does the $U(1)$ global symmetry break in the gauged $XY$ model?
I'm studying the particle vortex duality, and I'm confused how we're able to say that in the Coulomb phase, the "hidden" $U(1)$ global magnetic symmetry spontaneously breaks.
gauged XY model: $\...
- 737
1
vote
1
answer
108
views
Showing that the $\mathcal{N=2}$ SUSY Effective Action is Duality-Invariant
The effective action of the $\mathcal{N}=2$ supersymmetric $SU(2)$ gauge theory contains the following term;
$$Im\int d^{4}xd^{2}\theta d^{2}\bar{\theta}\Phi^{\dagger}\mathcal{F}'(\Phi)$$
Where $\Phi$ ...
- 577
5
votes
2
answers
620
views
Duality transformations, such as between a massless scalar field and the Kalb-Ramond field
There is a kind of duality transformations between antisymmetric tensor fields which I learnt from a series of lectures by Gia Dvali on quantum field theory. I have not been able to locate a source ...
- 2,568
1
vote
1
answer
159
views
Why do we consider solitons as a composite object?
Can someone explain why do we consider solitons as a composite object? I know that there are dual theories which the role of fundamental and solitonic objects can be mapped to each other, but I can't ...
- 49
2
votes
0
answers
99
views
Does a Chern-Simons term break the $F \rightarrow \star F$ symmetry?
When is the electro-magnetic duality $F \rightarrow \star F$ a symmetry of a theory? I know it holds for free Yang-Mills, but would for instance a Chern-Simons term break it or a coupling to matter? ...
- 125