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Questions tagged [duality]

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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 ...
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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\...
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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?
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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
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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
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
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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_\...
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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 ...
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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 ...
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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
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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
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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
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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|^...
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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
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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
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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
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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 ...
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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
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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
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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 ...
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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
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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}\...
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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 ...
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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}{...
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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 $...
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0answers
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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
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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 ...
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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. ...
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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 ...
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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
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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{\...
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4answers
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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
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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 ...
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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?
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0answers
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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 ...
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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 ...
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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, ...
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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
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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
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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
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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 ...