Questions tagged [duality]
The duality tag has no usage guidance.
2
votes
0answers
44 views
Is there any GENERAL symmetry behind holography and dualities?
Holography tells that a theory with gravity in D-dimensions is equivalent to a field theory in D-1 on the boundary. Similarly, after the second string revolution, we know there are symmetries called ...
1
vote
2answers
114 views
Energy momentum tensor of EM field written in symmetric form
I'm reading A. Zee's book, Einstein Gravity in a Nutshell. In problem 7 of chapter IV.2, it is said that the energy momentum tensor of the electromagnetic field
\begin{align}
T^{\mu\nu}=\eta_{\lambda\...
0
votes
1answer
20 views
How do the vector and scalar potentials transform under electromagnetic duality trnasfotmation?
Maxwell equations are invariant under the duality transformation. The electric and magnetic fields are defined in terms of these potentials. How do these potentials transform under duality?
1
vote
1answer
65 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 $\...
9
votes
4answers
463 views
What is intuitively the Hodge dual of a $p$-form?
Carroll in his textbook "Spacetime and geometry" defines the Hodge dual of a $p$-form $A$ on an $n$-dimensional manifold as $$(\star A)_{\mu_1...\mu_{n-p}}=\dfrac{1}{p!}\epsilon^{\nu_1...\nu_p} _{\ \ \...
2
votes
2answers
81 views
Duality transformations, such as between a massless scalar field and the Kalb-Ramond field
There is a kind of duality transformations between antisymmetric tensor fields which I learnt from a series of lectures by Gia Dvali on quantum field theory. I have not been able to locate a source ...
1
vote
0answers
21 views
Checking modularity-like transformation property
Assume $M$ is a 4 manifold. Let $Z_v$ be partition function of fixed magnetic flux $v$ with all instanton configuration summed over where $v\in H^2(M,Z/nZ)$. $\tau$ denotes complex parameter on upper ...
2
votes
0answers
67 views
Path Integral in Electric-Magnetic Duality
The action of electromagnetic field is
$$S=\int\left(-\frac{1}{2e^{2}}F\wedge\ast F+\frac{\theta}{8\pi^{2}}F\wedge F\right),$$
where $F=dA$ is the curvature $2$-form, and $A$ is the connection $1$-...
1
vote
1answer
67 views
Ising model and duality
I'm studying the Ising model in 2 dimensions in an approximative way. Now my professor has written this formula that links the dual space and the "normal" space:
$$\sinh(2 K) \sinh(2 K^*) = 1 $$
Do ...
1
vote
1answer
81 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 ...
0
votes
2answers
76 views
Dual of Kalb Ramond field [closed]
i've been studying string theory for 4 days, i have a Kalb Ramond $B_{(2)}$ of this kind (from a $5^2 _2$ solution [1]) and i want evaluate its dual but i don't obtain the right result:
The variables ...
9
votes
2answers
193 views
Chirality of the Electromagnetic Field Tensor
I have learned that chirality is a concept, that appears for $(A,B)$ representations of the Lorentz group, where $A\neq B$.
An example would be a Dirac spinor, corresponding to the representation $(\...
0
votes
1answer
93 views
A universe with fully symmetric electromagnetism?
Although several extensions to the Standard Model predict the possible existence of magnetic monopoles, their expected properties are rather significantly different from those of the electrically-...
1
vote
1answer
59 views
S Duality and Effective Couplings
I am brand new to this subject, so this will probably be a very stupid question, but I would appreciate any patient explanations.
S-duality is typically described as a relationship between two QFTs (...
8
votes
2answers
212 views
“$\theta$-$\phi$ duality” and $T$-duality
When bosonizing an interacting spinless Luttinger liquid, the action can be written as
\begin{equation}
S=\frac{K}{2\pi}\int dx d\tau\ (\partial_\mu\phi)^2 = \frac{1}{2\pi K}\int dx d\tau\ (\partial_\...
1
vote
0answers
48 views
What is U-duality? and Why U-duality is important?
In string theory, we know three dualities.
S-duality: Extension of Electric-magnetic duality, Duality between strongly coupled qft and weakly coupled qft. (One of the typical example is Seiberg ...
0
votes
0answers
21 views
The ultimate (SUSY) degrees of freedom and how to test them: particles, strings or something else?
I have been thinking about these question and if I should post it, because I want it to fit the rules of these site. Let's see if I managed it:
Are the ultimate degrees of freedom of the subatomic ...
1
vote
0answers
28 views
New-minimal vs old-minimal supergravity
New-minimal set of supergravity auxiliary fields includes a two-form field, whereas the old-minimal auxiliary set includes a vector and a complex scalar. Is anyone aware of how to transform between ...
1
vote
1answer
52 views
DBI action expansion for non-abelian brane worldvolume
I am trying to reproduce the results of the (famous) Myer's paper "Dielectric Branes" https://arxiv.org/abs/hep-th/9910053. In eq (33),
when he expands the determinant factor for a flat-space ...
4
votes
2answers
116 views
Special relativity constrains massless electric dipoles, but not massless magnetic dipoles?
Discussion in comments on the two questions linked below leaves me confused about the following point.
We expect a magnetic or electric dipole to make a field that has some universal transformation ...
2
votes
1answer
564 views
Wilson-Fisher Fixed Point in 2+1 Dimensions
In the paper by y Nathan Seiberg, T. Senthil, Chong Wang and Edward Witten,
A Duality Web in 2+1 Dimensions and Condensed Matter Physics
it is claimed on page 1 that the two theories
$$|D_{B}\phi|^...
0
votes
0answers
37 views
Sign on Particle-Vortex Duality from 3d Bosonization
This is most likely a question with a very simple answer but well, on the paper "Particle-Vortex Duality from 3d Bosonization" by Karch and Tong, on page 11 it is claimed that the first three terms on ...
3
votes
0answers
61 views
Does topological mass imply preservation of global symmetry whose current is topological?
This question is general but the motivation for it lies within the paper "A Duality Web in 2+1 Dimensions and Condensed Matter Physics". On pages 20-23, they consider a system which has four phases ...
5
votes
1answer
195 views
Why does a monopole operator break the global symmetry with topological current?
I am currently reading the paper "A Duality Web in 2+ 1 Dimensions and Condensed Matter Physics" by Seiberg et al, and on page 22 they add to the Lagrangian a monopole operator of the form $\phi^{\...
3
votes
1answer
66 views
Does a SUSY Chern-Simons term prevent the dualising of the gauge potential to a scalar?
In 3D $\mathcal{N}=2$ supersymmetric field theory with abelian gauge fields, the gauge field $A_{\mu}$ is often dualised to a real scalar $\gamma$. Does a Chern-Simons term prevent this dual ...
2
votes
0answers
74 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? ...
7
votes
0answers
348 views
Level-rank duality in WZW models and CS theories
Cross-posting from Physics Overflow: https://www.physicsoverflow.org/41281/level-rank-duality-in-wzw-models-and-cs-theories
I know that the classical level-rank duality in the $\widehat{\mathfrak{sl}}...
4
votes
1answer
125 views
What is really this Gauge-Gravity duality all about?
I have no background in string theory but have a reasonable exposure to quantum field theory including the quantization of gauge theories. In simple terms what is this Gauge-Gravity duality all about ...
0
votes
0answers
45 views
Multiple Classical Limits of a Quantum Theory [duplicate]
I recently learned that one of the many lessons that one can learn from the AdS/CFT correspondence is that there could be two classical limits (the bulk with gravity in $D+1$ spatial dimensions, and ...
2
votes
1answer
97 views
Peskin's duality in XY model (Mandelstam-'t Hooft duality in abelian lattice models)
I am studying the old paper by Peskin (1978): Mandelstam-'t Hooft duality in abelian lattice models (https://doi.org/10.1016/0003-4916(78)90252-X). However, I am confused about some details of ...
2
votes
1answer
93 views
Physical implication of $\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\rightarrow -\textbf{E}$ invariance of the Maxwell's equations
An interesting observation to consider about the Maxwell's equation is that in absence of the sources, the equations are symmetric under the interchange $$\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\...
1
vote
1answer
129 views
How can the information encoded in a boundary be changed in holographic principle?
When information is encoded in a lower dimensional boundary of a bulk, following the holographic principle, it would raise a universe in the boundary with physics determined by the information encoded ...
1
vote
0answers
58 views
The Action for Electric-Magnetic Duality
In the paper A Duality Web in 2+1 Dimensions and Condensed Matter Physics on page 34, the action for electromagnetic field in Lorentzian signature is given by
$$S=\int d^{4}x\sqrt{-g}\left(\frac{-1}{...
4
votes
0answers
162 views
Question about Monopole Operator
I've been studying IR-dualities in 2+1 dimensions. I encountered monopole operators in the following paper:
Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)d
On page 10, starting from $...
2
votes
0answers
70 views
A Question about Abelian Dualities in 2+1 Dimensions
I have a question from the paper
More Abelian Dualities in 2+1 Dimensions.
On page 3, it says that we flow towards IR by sending $\alpha\rightarrow\infty$ and tuning the mass to zero.
$$S[\phi ;A]...
10
votes
1answer
348 views
What is really M-theory? (non-pertubatively)
I don´t really understand what M-theory is supposed to be. Going beyond the dualities relating different string theories (for example the common $11-D$ limit of IIA and $E_{8}\times E_{8}$) I don't ...
1
vote
1answer
254 views
How does holographic duality work?
In holographic theories about the universe, the one being in the boundary of the space, takes information of the higher dimensional universe, so, two different theories can describe the two universes.
...
-1
votes
2answers
61 views
particle wave duality [duplicate]
A single photon travelling within a single wavelength contains a dual nature, in that it can behave as a particle or a wave depending upon the chosen experiment or measure.
When the duality behaves ...
-2
votes
1answer
128 views
What is fundamental in the AdS/CFT holographic universe formulation of String theory?
I have a lot of confusion about the AdS/CFT with holography. Does it show that strings and branes are excitations of fields on the conformal boundary of the universe (CFT)?
Can someone explain the AdS/...
0
votes
1answer
132 views
Why aren't Faraday's law of induction and Maxwell-Ampere's law symmetric? [duplicate]
I don't see Faraday's law of induction and Maxwell-Ampere's law are totally symmetric in the sense that Maxwell-Ampere's law has a
factor of $ϵ_0μ_0$:
\begin{align}
\nabla\times\mathbf E&=-\frac{\...
6
votes
4answers
1k views
Why are position and momentum space examples of Pontryagin duality?
https://en.wikipedia.org/wiki/Position_and_momentum_space
https://en.wikipedia.org/wiki/Pontryagin_duality
I am trying to understand logic behind the uncertainity principle. And as far as I ...
6
votes
1answer
148 views
A fundamental question about Seiberg duality
Standard set up and review:
Let us consider $SU(N)$ SQCD with $N_f$ flavors as our electric theory (just like in Seiberg's paper) and also let $N_f \geq N$. This theory is completely Higgsed in the ...
0
votes
0answers
116 views
Do Liouville theory have a gravity dual?
Does Liouville theory have a gravity dual? I think the answer is not. But what's wrong with Liouville theory?
What features of Liouville theory are universal for other CFTs?
3
votes
0answers
57 views
Possible string duality example?
One can consider the Calabi-Yau threefold K3$\times E$ where the Donaldson-Thomas theory is conjectured to be the (inverse of) the Igusa cusp form $\chi_{10}(q,y,p)$. The variables $q,y,p$ aren't ...
10
votes
0answers
191 views
How does one actually apply the M-theory/heterotic duality “fiberwise”?
It seems to be generally accepted ([1], [2]) that one can apply the duality between a $T^3$ compactification of heterotic string theory and a $\mathrm{K3}$ compactification of M-theory "fiberwise" to ...
1
vote
1answer
183 views
Wilson loop in AdS/CFT : string interpretation
It is well known that Wilson loop is a quite hard observable to compute. In the case in which the QFT is dual to a gravitation theory in AdS space, we can use holography to compute the Wilson loop, ...
0
votes
2answers
140 views
CFT energy scale in AdS/CFT correspondence
In the context of the AdS/CFT correspondence, the coordinate $z$ of AdS in Poincarè coordinates is often identified with an (inverse) energy scale for a CFT. I don't quite understand this ...
4
votes
1answer
233 views
Is there either a Lagrangian or a Hamiltonian formulation of electromagnetism with continuous distributions of magnetic monopoles?
Maxwell's equations generalize very nicely if we add in magnetic monopoles: we get
$$\begin{align*}
\partial_\mu F^{\mu \nu} &= J^\nu \\
\partial_\mu \tilde{F}^{\mu \nu} &= \tilde{J}^\nu,
\end{...
2
votes
1answer
366 views
Tensor Formulation of Maxwell's Equations
I've been reading up about the tensor formulation of Maxwell's Equations of Electromagnetism, and the derivations I have seen (found here: http://www.lecture-notes.co.uk/susskind/special-relativity/...
4
votes
2answers
78 views
What is the mass of an electron in the sense of its wave nature?
I just completed a course in Mechanics and I'm currently doing electromagnetism. I haven't rigorously started QM; or Modern Physics. I read up a few articles on the Wave-Particle duality.
So, how is ...
