Questions tagged [duality]

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55
votes
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' ...
10
votes
1answer
613 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 ...
16
votes
2answers
4k 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} \...
15
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^...
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 ...
4
votes
1answer
507 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
242 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{...
1
vote
3answers
1k views

Why aren't Faraday's law of induction and Maxwell-Ampere's law (without sources) symmetric?

I was wondering why Faraday's law of induction and Maxwell-Ampere's law (without sources) are not totally symmetric in the sense that Maxwell-Ampere's law has a $\epsilon_0 \mu_0$ term on the right (...
5
votes
1answer
435 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-...
19
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 ...
11
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 ...
8
votes
0answers
248 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 ...
9
votes
2answers
208 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 $(\...
6
votes
2answers
616 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 ...
0
votes
1answer
96 views

Electro-mangetic duality, Quantum electro dynamics and N=4 SYM

This question is extension of Electro magnetic duality, Strong weak duality and N=4 super Yangmils which i asked before. Here what i want to know is compare of QED and N=4 SYM in terms of electro-...
1
vote
1answer
134 views

Electro magnetic duality, Strong weak duality and N=4 super Yangmils

How we can interpret this self-dual, or duality in terms of generalized version of electro magneitc duality, or Strong weak duality. Let me address some basic information. First, electro magnetic ...
6
votes
0answers
134 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
522 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 ...
2
votes
1answer
95 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}\...
2
votes
4answers
13k views

Relationship between Energy and Time [closed]

Is there a relationship between energy and time? What is it?
4
votes
2answers
122 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
0answers
76 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? ...
1
vote
3answers
473 views

What does the “T” stand for in T-duality?

First of all, I am not a physicist. I'm a graduate math student and recently I came across the concept of T-duality. Actually I'm studying generalized complex geometry, which according to this paper (...
1
vote
1answer
366 views

What would Maxwell's Equations be if we had magnetic charges and magnetic currents?

Mind you, we still have electric charge and electric currents. But, what would Maxwell's equations look like if we had to take magnetic charges and magnetic currents into consideration? Would there be ...
1
vote
1answer
306 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. ...