Questions tagged [duality]

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1answer
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Duality between gravitation and $O(N)$ model

Does there exist any gravity dual theory for theory with $N$-component scalar field with $(\phi^2)^2$ interaction?
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0answers
16 views

Dualities involving Supersymmetric QED in $3+1$d

Most of the supersymmetric dualities in $3+1$d involve only non-Abelian gauge theories, like $SU(N)$ $\mathcal{N}=1$ SQCD, etc. Are there examples of dualities which involve supersymmetric QED (i.e. ...
3
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1answer
67 views

How does the $U(1)$ global symmetry break in the gauged $XY$ model?

I'm studying the particle vortex duality, and I'm confused how we're able to say that in the Coulomb phase, the "hidden" $U(1)$ global magnetic symmetry spontaneously breaks. gauged XY model: $\...
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1answer
20 views

Complementary channel of convex combination of channels

Consider two channels $N_1$ and $N_2$ which have Kraus operators $\{A_k\}$ and $\{B_k\}$ respectively, where the index $k$ runs over the number of Kraus operators. Define a third channel $N$ as a ...
4
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1answer
98 views

Symmetry of Maxwell equations for electric-magnetic duality

According to Griffiths's book on electrodynamics, including magnetic charge the Maxwell equations become $$ \begin{align*} \nabla \cdot \vec{E} &= \frac{\rho_e}{\epsilon_0} &&& \nabla ...
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1answer
119 views

The Zero Energy Hypothesis and its consequences for particle creation and dualist interactionism

Most attacks on the possibility of dualist interaction cite the conservation of energy as a definitive objection. I have attempted to investigate the validity of this objection, and have found a ...
3
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0answers
63 views

A Question about Wave-Function Renormalization Factor in SQCD

Here, I have a question about the one-loop computation of the wave-function renormalization factor in SQCD. According to Seiberg duality, the following electric $\mathrm{SQCD}_{e}$ \begin{gather} ...
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0answers
48 views

Different duality-correlations in holographic principle?

I found an interesting article "Surface/State Correspondence as a Generalized Holography" (https://arxiv.org/abs/1503.03542) If I understood it well, the authors proposed this model to generalize the ...
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1answer
76 views

Is the gauge/gravity (or AdS/CFT) duality believed to be exact?

I was wondering about the implications of the gauge/gravity (or AdS/CFT in a more restrictive sense) duality for the way we deal with physical theories, and I was wondering if the duality was believed ...
3
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1answer
84 views

Charge-Vortex Duality for Bosons

Consider a (2+1)d continuum field theory with the Minkowski action $$\mathcal{L}=|\partial\phi|^2-r|\phi|^2-u|\phi|^4,$$ where $\phi$ is a complex field. The theory undergoes a quantum phase ...
3
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0answers
53 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 ...
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2answers
140 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
21 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
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1answer
71 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
909 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
106 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 ...
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0answers
74 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
85 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
83 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 ...
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2answers
93 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
219 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
101 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
62 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 (...
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2answers
255 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
53 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
34 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
61 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
126 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
753 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
66 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 ...
6
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1answer
233 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
67 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
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0answers
78 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
394 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
143 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
46 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
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1answer
117 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
98 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
130 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
63 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
195 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
74 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
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1answer
369 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
329 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
64 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
136 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/...
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1answer
152 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
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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
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1answer
160 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 ...