Questions tagged [duality]

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4
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1answer
122 views
+50

The planar limit, self-duality and their relation to two dimensions

In the lecture notes by Beisert on integrability, it is stated that integrability is a property mainly in two-dimensional field theories, with some higher-dimensional examples. As higher-dimensional ...
1
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1answer
38 views

Is superstrings on the $E_8$ torus dual to bosonic string theory on the Leech lattice torus?

Two important unimodular lattices are $E_8$ and the Leech lattice. One can take 10D superstring theory and compactify it over the $E_8$ torus. One can also take 26D bosonic string theory and ...
2
votes
1answer
135 views

Electromagnetic duality interacting with a complex scalar field

My question refers to example theory introduced in the book "Supergravity" from D.Z.Freedman & A. van Proeyen p.80. Its Lagrangian is given by $${\cal L}(Z,F) =-\frac{1}{4}(Im Z)F_{\mu\...
7
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2answers
142 views

Can supersymmetries change under dualities, like gauge symmetries can?

Symmetries that have non-trivial effects on observables must be preserved by dualities (equivalences between different-looking quantum field theories), because the equivalence relation preserves ...
2
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1answer
99 views

Why does T-duality not create consistent string theories below the critical dimension?

As I know it, T-duality essentially tells us that if we compactify a superstring theory on a circle of radius $R$, it is equivalent to a string theory compactified on a circle of radius $\tfrac{\alpha'...
2
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0answers
35 views

Bern-Carrasco-Johansson (BCJ) Double Copy and Color-Kinematic duality

According to the wikipedia page on Strong Gravity, the theory is considered "non-mainstream", but from what I can gather there have been some very interesting progress and results since it ...
3
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2answers
102 views

Can we define a vector potential for $E$-Field in Empty Space?

In deriving the Electromagnetic wave equation in free space we remove all charge sources. The resultant Maxwell vector equations are thus source-free. Using Gaussian units with the speed of light $c=1$...
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0answers
30 views

Can $\mathcal{N}=4$ SYM be interpreted as describing a superconductor?

I am quite fond of analogies between QFT and statistical mechanics, although I am not at all an expert in statistical physics. And I was wondering if it would make any sense to view the (Euclidean) ...
2
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0answers
37 views

free fermion- monopole operator in scalar $QED_3+$ Chern simons term equivalence proof?

In most papers discussing 3D Abelian bosonization duality, they say that monopole operator in scalar $QED_3+CS$ is dual to free fermions. How do they know it, because I have never seen an actual ...
2
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0answers
26 views

Interpretation of two independet solutions of equations of motion in AdS/CFT

I am trying to understand the statement in AdS/CFT correspondence, that from the two independent solutions of equations of motion in the bulk, one corresponds to the source of operator $\mathcal{O} (x)...
1
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3answers
170 views

Dual EM field in terms of original EM field [closed]

In Maxwell theory we have dual description in terms of dual fields: $$ \tilde{F}_{\mu\nu} = \partial_\mu \tilde{A}_\nu - \partial_\nu \tilde{A}_\mu = \varepsilon_{\mu\nu\rho\sigma} F^{\rho\sigma} $$ $...
1
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1answer
113 views

Legendre transformation in QFT

I know that given the Hamiltonian of a theory, there can be many different associated Lagrangians, or even none at all, but why is that so? In classical mechanics the Hamiltonian and Lagrangian ...
3
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1answer
101 views

Bulk/boundary duality for matter fields?

Usually, in gauge/gravity duality we have some CFT on a boundary that is dual to a gravity in the bulk. Although CFT is never written in Lagrangian form, it seems for me, that AdS/CFT correspondence ...
6
votes
1answer
89 views

Are dualities in QFT just change of variables?

Although a lot is usually said about dualities in QFT, this question doesn't seem to have any straightforward answer in most of the references. When we talk about dualities between QFTs what do we ...
7
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2answers
249 views

Is there an analogy for Wilson loops/lines in statistical mechanics?

When reformulated in Euclidean space, quantum field theory bears some strong resemblance to statistical mechanics: for example a scalar field $\phi$ can be seen as a spin $s$ in Landau theory, and the ...
4
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0answers
154 views

Constructing a Hubbard-Stratonovich Transform that goes from a theory of Electrostatics to a theory like Magnetostatics

I'm talking about a completely classical theory. Suppose I start with $$H = \int(\nabla \phi)^2 $$ I am talking about calculation of the partition function here $$Z = \int D[\phi] e^{(-\beta\int(\...
1
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0answers
42 views

String length vs. UV completion

In string theory, we have a fundamental length $l_s$. From T-duality, we expect a duality between UV and IR; a length smaller than $l_s$ is regarded as a length greater than $l_s$. We do not see any ...
2
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0answers
65 views

$T$-duality symmetry of $SU(2)_1$ WZW model

For bosons at self-dual radius, the CFT has T-duality symmetry. My question is can we realize this symmetry on the lattice model? for example antiferromagnetic spin chain.
1
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2answers
219 views

What is the difference between a dual vector and a reciprocal vector?

I am familiar with the concept of a dual space $V^*$ as the set of all linear functionals $\tilde{\omega}: V \rightarrow \mathbb{R}$. The inner product on $V$ is usually used to define the dual of a ...
4
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1answer
86 views

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?
2
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0answers
23 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. ...
4
votes
1answer
154 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: $\...
0
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1answer
33 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 ...
5
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1answer
315 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 ...
-2
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1answer
145 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
153 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
49 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 ...
1
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1answer
119 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 ...
5
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1answer
186 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
59 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
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2answers
240 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
31 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
78 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 $\Phi$ ...
12
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4answers
2k 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
201 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
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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
87 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
171 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
103 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
124 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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3answers
356 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
110 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-...
2
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1answer
79 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 (...
9
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2answers
367 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_\...
2
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1answer
76 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 ...
2
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0answers
53 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
110 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 ...
5
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2answers
155 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 ...
4
votes
1answer
1k 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|^...
3
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0answers
77 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 ...