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Questions tagged [duality]

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54
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10answers
11k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' ...
47
votes
6answers
13k views

Why do lasers cut? Is this a case of light acting as matter?

All I found in Google was very broad. From a physics models perspective, why can photons emitted from a laser cut? Does this cut mean that the photons are acting like matter?
25
votes
1answer
583 views

“S-duality” between confinement and the Higgs mechanism?

I feel picked by the second to last sentence in this answer to a question about what would happen if EM and QCD were spontaneously broken, which says "In fact, there is a sense in theoretical ...
20
votes
5answers
2k views

Is quantum mechanics intrinsically dualistic?

In just about every interpretation of quantum mechanics, there appears to be some form of dualism. Is this inevitable or not? In the orthodox Copenhagen interpretation by Bohr and Heisenberg, the ...
18
votes
3answers
249 views

Paper listing known Seiberg-dual pairs of N=1 gauge theories

Is there a nice list of known Seiberg-dual pairs somewhere? There are so many papers from the middle 1990s but I do not find comprehensive review. Could you suggest a reference? Seiberg's original ...
18
votes
2answers
2k views

Confusion about duality transformation in 1+1D Ising model in a transverse field

In 1+1D Ising model with a transverse field defined by the Hamiltonian \begin{equation} H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x \end{equation} There is a duality transformation which ...
15
votes
2answers
3k views

What's the intuition behind the Choi-Jamiolkowski isomorphism?

What is the intuition behind the Choi-Jamiolkowski isomorphism? It says that with every superoperator $\mathbb{E}$ we can associate a state given by a density matrix $$ J(\mathbb{E}) = (\mathbb{E} \...
14
votes
1answer
2k views

When one discusses the “boundary” of Anti-de Sitter space, what do they mean precisely?

The AdS/CFT correspondence refers to the "boundary" of AdS space but I'm a little confused about what this means. Typically, one writes the AdS metric in the form $ds^2= \frac{L^2}{z^2}(-dt^2+d\vec x^...
13
votes
1answer
121 views

Local Fermionic Symmetry

That is perhaps a bit of an advertisement, but a couple of collaborators and myself just sent out a paper, and one of the results there is a little bit surprising. We found (in section 6E) a fermionic ...
11
votes
2answers
2k views

Advanced topics in string theory

I'm looking for texts about topics in string theory that are "advanced" in the sense that they go beyond perturbative string theory. Specifically I'm interested in String field theory (including ...
11
votes
2answers
669 views

Is the U(1) gauge theory in 2+1D dual to a U(1) or an integer XY model?

The compact U(1) lattice gauge theory is described by the action $$S_0=-\frac{1}{g^2}\sum_\square \cos\left(\sum_{l\in\partial \square}A_l\right),$$ where the gauge connection $A_l\in$U(1) is defined ...
10
votes
3answers
2k views

Symmetry in electricity and magnetism due to magnetic monopoles

I was wondering about the differences between electricity and magnetism in the context of Maxwell's equations. When I thought over it, I came to the conclusion that the only difference between the two ...
10
votes
1answer
594 views

Effect of introducing magnetic charge on use of vector potential [duplicate]

It is well known that Maxwell equations can be made symmetric w.r.t. $E$ and $B$ by introducing non-zero magnetic charge density/flux. In this case we have $div B = \rho_m$, where $\rho_m$ is a ...
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 ...
9
votes
4answers
431 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} _{\ \ \...
9
votes
1answer
265 views

What evidence do we have for S-duality in N=4 Super-Yang-Mills?

Do we have anything resembling a proof*? Or is it just a collection of "coincidences"? Also, do we have evidence from lattice gauge theory computations? *Of course I'm not talking about a proof in ...
9
votes
2answers
192 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 $(\...
9
votes
1answer
86 views

Dual Pairs in Four Dimensions

Following the conversation here, I am wondering if anyone knows of an example of dual pair with 4-dimensional N=1 SUSY which relates a non-Abelian gauge theory on one side to a theory with a ...
9
votes
1answer
345 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 ...
8
votes
2answers
1k views

Why is a stack of N D-branes equivalent to an extremal black brane?

A stack of N D-branes can have open strings ending on them. There is a U(N) brane gauge field, and r adjoint Higgs fields, with r equal to the number of transverse spatial dimensions. The eigenvalues ...
8
votes
1answer
2k views

$N=4$ supersymmetric yang-mills theory and S-duality

[Question suggested by @Lawrence B. Crowell's answer to the question on T-duality] There are three parts to my question: A. What is the action for $N=4$ SUSY Yang-Mills and what is the physics of ...
8
votes
2answers
211 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_\...
8
votes
1answer
208 views

Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?

Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
8
votes
0answers
243 views

Intuition for Homological Mirror Symmetry

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
7
votes
1answer
175 views

Mathematical content of Thirring/Sine-Gordon duality

I'm a mathematician who is intrigued by the duality between the Thirring and Sine-Gordon models as established by Sidney Coleman. Can someone explain the mathematical content of this duality to me? (...
7
votes
0answers
346 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}}...
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
2answers
599 views

T-duality approaches

The textbook approach to explaining T-dualities is to show that a type of T-duality transformation "inverts the radius of the circle, that is, it maps $R\rightarrow\tilde{R} = \alpha'/R$ and it ...
6
votes
2answers
2k views

If electrons behave as standing waves when they are bound to an atom then how do they carry charge?

Today in my physics lesson we learnt that the best way of describing the behaviour of an electron that is bound to an atom is to treat it as a standing wave. I understand that this is the wave-...
6
votes
1answer
394 views

Uniqueness of the 5 string theories

This question combines several sub-questions, the common theme being: why the known 5 string theories are unique? Firstly, regarding heterotic theory. I understand the only allowed gauge groups are $...
6
votes
1answer
181 views

Why is there no double counting of $s$- and $t$-channels in string theory?

In string theory for the four particle tree diagram exchange, why is there some mysterious crossing duality between the $s$- and $t$- and $u$-channels? Why isn't there a double counting in the Feynman ...
6
votes
1answer
147 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 ...
6
votes
0answers
133 views

String landscape in different dimensions

For D = 11 large (uncompactified) spacetime dimensions, the only "string theory" vacuum is M-theory For D = 10, there are 5 vacua. Or maybe it's more correct to say 4, since type I is S-dual to $Spin(...
5
votes
1answer
518 views

${f=ma}$: a duality between F-theory and M-theory?

$$F = M \Big|_{A(T^2) \to 0}$$ The above equation is the duality equation between F-theory and M-Theory on a vanishing 2-torus. What's the explanation for this equation? Is there anything similar ...
5
votes
2answers
344 views

Proof of S-duality between Type IIB, IIB and Type HO, I string theories

About every source on string theory I've read which do mention S-duality state that: $$\begin{array}{l} \operatorname S:\operatorname{IIB} \leftrightarrow \operatorname{IIB}\\ \operatorname S:\...
5
votes
2answers
334 views

Definition of Duality (opposed to Symmetry)

I'm learning basic string theory right now and we came across T-duality which was presented as a symmetry of the formula for the mass of a string in the context of compactification. There was a remark ...
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^{\...
5
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{...
5
votes
1answer
287 views

Why is Seiberg duality called an electromagnetic duality?

An electromagnetic duality is a duality that maps electric to magnetic degrees of freedom of two distinct theories. Apart from source-less Maxwell electrodynamics, other theories require magnetic ...
5
votes
1answer
127 views

AdS/CFT dual of $N$ D$p$-branes at finite temperature

The gravity dual of $N$ D$p$-branes at zero temperature is $$ ds^2= H^{-1/2}(r)(-dt^2+dx_p^2) + H^{1/2}(r)(dr^2 + r^2d\Omega_{8-p}^2) $$ with $$ H(r) = 1 + \left(\frac{R}{r}\right)^{7-p} $$ what ...
5
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 ...
5
votes
0answers
133 views

Yang-Mills/topological string theory (M-theory) duality

It is known that there is a duality between Chern-Simons theory on 3-fold $X$ and topological A-model on the cotangent bundle of this manifold, $T^*X$ (see, for example, the original paper by Witten, ...
5
votes
0answers
59 views

Baryonic operators in ${\cal N}=1$ $U(N)$ SQCD in four dimensions

Seiberg's duality is usually considered as a duality for $SU(N_c)$ theories with $N_f$ flavors. In his case, the vacuum for $N_f \geq N_c$ is parameterized by mesons $M$ and baryons ${\bar B}$ and $B$....
4
votes
1answer
502 views

T-Duality between Type HE String theory and Type HO string theory

My question is regarding T-Duality between the 2 Type H string theories. I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so $$\...
4
votes
1answer
395 views

Action with self-dual field strength

It is said that writing down an action in presence of a self-dual field strength is subtle and not known till date. The familiar example people give is that of type IIB super-gravity which has a self-...
4
votes
1answer
277 views

Why are electric charges allowed to be so light but magnetic monopoles have to be so heavy?

My question is in two parts. What is the origin of the electric field from an electric charge and why electron can have so small mass? While on the other hand for a magnetic monopole to create a ...
4
votes
2answers
311 views

Does the existence of dualities imply a more fundamental structure?

I was wondering if the existence of some kind of duality in physics always implies the existence of some underlying more fundamental structure/concept? Let me give a few example from history: Wave-...
4
votes
2answers
77 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 ...
4
votes
1answer
71 views

Quantum Mechanics: Relate solutions for two dual hamiltonians?

Consider a Hamiltonian in quantum mechanics: $$H_x=-\frac{d^2}{dx^2}+V(x,c)$$ where $x\in\mathbb{R}$ and the potential $V(x,c)$ depends on position $x$ and a continuous parameter $c$. Furthermore, ...
4
votes
1answer
124 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 ...