Questions tagged [duality]
The duality tag has no usage guidance.
180
questions
5
votes
1answer
69 views
What would it mean if symmetries are not fundamental at all?
In this paper 1 written by Joseph Polchinski, he seems to indicate that all symmetries of nature may not be fundamental:
From more theoretical points of view, string theory appears to allow no exact ...
4
votes
1answer
133 views
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
vote
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
136 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
votes
2answers
143 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
votes
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
votes
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
votes
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$...
1
vote
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
votes
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
votes
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
vote
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}
$$
$...
1
vote
1answer
113 views
Legendre transformation in QFT
I know that given the Hamiltonian of a theory, there can be many different associated Lagrangians, or even none at all, but why is that so? In classical mechanics the Hamiltonian and Lagrangian ...
3
votes
1answer
101 views
Bulk/boundary duality for matter fields?
Usually, in gauge/gravity duality we have some CFT on a boundary that is dual to a gravity in the bulk. Although CFT is never written in Lagrangian form, it seems for me, that AdS/CFT correspondence ...
6
votes
1answer
89 views
Are dualities in QFT just change of variables?
Although a lot is usually said about dualities in QFT, this question doesn't seem to have any straightforward answer in most of the references. When we talk about dualities between QFTs what do we ...
7
votes
2answers
249 views
Is there an analogy for Wilson loops/lines in statistical mechanics?
When reformulated in Euclidean space, quantum field theory bears some strong resemblance to statistical mechanics: for example a scalar field $\phi$ can be seen as a spin $s$ in Landau theory, and the ...
4
votes
0answers
154 views
Constructing a Hubbard-Stratonovich Transform that goes from a theory of Electrostatics to a theory like Magnetostatics
I'm talking about a completely classical theory.
Suppose I start with
$$H = \int(\nabla \phi)^2 $$
I am talking about calculation of the partition function here
$$Z = \int D[\phi] e^{(-\beta\int(\...
1
vote
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
votes
0answers
66 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
vote
2answers
222 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
votes
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
votes
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
155 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
votes
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
votes
1answer
316 views
Symmetry of Maxwell equations for electric-magnetic duality
According to Griffiths's book on electrodynamics, including magnetic charge the Maxwell equations become
$$
\begin{align*}
\nabla \cdot \vec{E} &= \frac{\rho_e}{\epsilon_0} &&&
\nabla ...
-2
votes
1answer
146 views
The Zero Energy Hypothesis and its consequences for particle creation and dualist interactionism
Most attacks on the possibility of dualist interaction cite the conservation of energy as a definitive objection. I have attempted to investigate the validity of this objection, and have found a ...
3
votes
0answers
154 views
A Question about Wave-Function Renormalization Factor in SQCD
Here, I have a question about the one-loop computation of the wave-function renormalization factor in SQCD.
According to Seiberg duality, the following electric $\mathrm{SQCD}_{e}$
\begin{gather}
...
1
vote
0answers
49 views
Different duality-correlations in holographic principle?
I found an interesting article "Surface/State Correspondence as a Generalized Holography" (https://arxiv.org/abs/1503.03542)
If I understood it well, the authors proposed this model to generalize the ...
1
vote
1answer
120 views
Is the gauge/gravity (or AdS/CFT) duality believed to be exact?
I was wondering about the implications of the gauge/gravity (or AdS/CFT in a more restrictive sense) duality for the way we deal with physical theories, and I was wondering if the duality was believed ...
5
votes
1answer
187 views
Charge-Vortex Duality for Bosons
Consider a (2+1)d continuum field theory with the Minkowski action
$$\mathcal{L}=|\partial\phi|^2-r|\phi|^2-u|\phi|^4,$$
where $\phi$ is a complex field. The theory undergoes a quantum phase ...
3
votes
0answers
59 views
Is there any GENERAL symmetry behind holography and dualities?
Holography tells that a theory with gravity in D-dimensions is equivalent to a field theory in D-1 on the boundary. Similarly, after the second string revolution, we know there are symmetries called ...
1
vote
2answers
240 views
Energy momentum tensor of EM field written in symmetric form
I'm reading A. Zee's book, Einstein Gravity in a Nutshell. In problem 7 of chapter IV.2, it is said that the energy momentum tensor of the electromagnetic field
\begin{align}
T^{\mu\nu}=\eta_{\lambda\...
0
votes
1answer
31 views
How do the vector and scalar potentials transform under electromagnetic duality trnasfotmation?
Maxwell equations are invariant under the duality transformation. The electric and magnetic fields are defined in terms of these potentials. How do these potentials transform under duality?
1
vote
1answer
78 views
Showing that the $\mathcal{N=2}$ SUSY Effective Action is Duality-Invariant
The effective action of the $\mathcal{N}=2$ supersymmetric $SU(2)$ gauge theory contains the following term;
$$Im\int d^{4}xd^{2}\theta d^{2}\bar{\theta}\Phi^{\dagger}\mathcal{F}'(\Phi)$$
Where $\Phi$ ...
12
votes
4answers
2k views
What is intuitively the Hodge dual of a $p$-form?
Carroll in his textbook "Spacetime and geometry" defines the Hodge dual of a $p$-form $A$ on an $n$-dimensional manifold as $$(\star A)_{\mu_1...\mu_{n-p}}=\dfrac{1}{p!}\epsilon^{\nu_1...\nu_p} _{\ \ \...
2
votes
2answers
206 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
vote
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
votes
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
vote
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
vote
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
votes
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
votes
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 $(\...
0
votes
1answer
110 views
A universe with fully symmetric electromagnetism?
Although several extensions to the Standard Model predict the possible existence of magnetic monopoles, their expected properties are rather significantly different from those of the electrically-...
2
votes
1answer
79 views
S Duality and Effective Couplings
I am brand new to this subject, so this will probably be a very stupid question, but I would appreciate any patient explanations.
S-duality is typically described as a relationship between two QFTs (...
9
votes
2answers
367 views
“$\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
votes
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
votes
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
vote
1answer
111 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
votes
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|^...
