Questions tagged [duality]
The duality tag has no usage guidance.
248
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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
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Does there exist a duality between the following two quantum systems?
Consider two systems:
A) $N$ number of independent spin $0$ bosons living on a circle.
B) A single spin $0$ boson moving on an $N$-torus.
How do we detect the difference between the two systems ...
user77187
2
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0
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122
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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(...
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Why is the Jordan-Wigner transformation an example of an S-duality?
The Jordan-Wigner transformation allows one to map a spin theory to a fermionic theory and, according to wikipedia, it is an example of an S-duality. In turn, according to the wiki page for the S-...
- 1,544
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Kramers-Wannier duality high and low temperature expansions confusion
I am reading the section on the 2D Ising model Krammer-Wannier duality in the book Exactly Solved Models in Statistical Mechanics (pg. ~76) by R.J. Baxter. I have two questions:
What was the ...
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2
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559
views
Deriving conserved charges from the equations of motion
It is very well established how to derive conserved charges associated to the symmetries of Lagrangian using the Noether's theorem. Also in the Hamiltonian formulation, we know how to derive the ...
- 980
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One-loop exactness of self-dual Yang-Mills theory
The self-dual Yang-Mills theory (gauge group $G$) with the action:
$$
\mathcal{S} = \int_{M} \text{Tr} (B^{+} \wedge F)
$$
where $B^{+}$ is a self-dual field, transforming in the adjoint ...
- 4,883
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What would it mean if symmetries are not fundamental at all?
In this paper 1 written by Joseph Polchinski, he seems to indicate that all symmetries of nature may not be fundamental:
From more theoretical points of view, string theory appears to allow no exact ...
- 2,462
5
votes
1
answer
243
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Anomalies in the self-dual Yang-Mills theory and $\mathcal{N}=2$ open-string theory
I am reading a paper, written by G. Chalmers and W. Siegel - https://arxiv.org/abs/hep-th/9606061, where they discuss the action of self-dual Yang-Mills theory, which in light-cone formalism is ...
- 4,883
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The planar limit, self-duality and their relation to two dimensions
In the lecture notes by Beisert on integrability, it is stated that integrability is a property mainly in two-dimensional field theories, with some higher-dimensional examples. As higher-dimensional ...
user172341
3
votes
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Is superstrings on the $E_8$ torus dual to bosonic string theory on the Leech lattice torus?
Two important unimodular lattices are $E_8$ and the Leech lattice.
One can take 10D superstring theory and compactify it over the $E_8$ torus.
One can also take 26D bosonic string theory and ...
user84158
2
votes
1
answer
280
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Electromagnetic duality interacting with a complex scalar field
My question refers to example theory introduced in the book "Supergravity" from D.Z.Freedman & A. van Proeyen p.80. Its Lagrangian is given by
$${\cal L}(Z,F) =-\frac{1}{4}(Im Z)F_{\mu\...
- 9,778
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Can supersymmetries change under dualities, like gauge symmetries can?
Symmetries that have non-trivial effects on observables must be preserved by dualities (equivalences between different-looking quantum field theories), because the equivalence relation preserves ...
- 54.5k
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Why does T-duality not create consistent string theories below the critical dimension?
As I know it, T-duality essentially tells us that if we compactify a superstring theory on a circle of radius $R$, it is equivalent to a string theory compactified on a circle of radius $\tfrac{\alpha'...
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Bern-Carrasco-Johansson (BCJ) Double Copy and Color-Kinematic duality
According to the wikipedia page on Strong Gravity, the theory is considered "non-mainstream", but from what I can gather there have been some very interesting progress and results since it ...
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