Questions tagged [duality]

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Regarding a possible duality between (2+1)D gravity and Chern-Simons Theory

Is there a duality between (2+1)D gravity and Chern-Simons Theory? Or they merely have related features? If so, of which type and why? Thanks!
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Dualities in Physics and Fourier Transforms

In many articles, authors compare physical dualities to Fourier transforms. For example: Joseph Polchinski, in his article "String Duality" (hep-th/9607050v2), writes: "Weak/strong ...
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At what coordinate is the D-brane located in the T dual world?

I have a simple question on the geometrical intuition of D branes. I am currently reading the TASI notes by Polchinski. Say one has a bosonic open string with all Neumann boundary conditions and ...
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88 views

What is $\mu_5$ in string theory?

I have come across the quantity $\mu_5$ in string theory quite a lot but I have not found it explicitly defined anywhere. The bosonic worldvolume action reads [1] \begin{equation} S = \frac{\mu_5}{g_s}...
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138 views

$T$-duality in effective gauge theories of a $D(p+1)$-brane

I am considering a $D(p+1)$-brane in a space $\mathbb R^{1,p}\times S_R^1$ where $S_R^1$ is the circle of radius $R$. I am assuming low energies $ER\ll1$, so that only the massless spectrum of the ...
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123 views

Transformation of the string coefficient under T-duality

I am trying to study an effective string theory valid in the low energy limit $ER<<1$. The effective action corresponds to a $D(p+1)$-brane in $R^{1,p}\times S^1$ and it is given by $$S_{D(p+1)} ...
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How to calculate the “vortex” correlation function in 2D free system?

I want to calculate the following correlation function in 2D square lattice: $$G(i, j, \tau) \equiv\left\langle e^{-\frac{i}{2}\left[\hat{\Phi}_{i}(\tau)-\hat{\Phi}_{j}(0)\right]}\right\rangle_{0}$$ $\...
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1answer
179 views

Can Montonen-Olive duality be used for studying $\mathcal{N}=4$ SYM at strong coupling? If not, why not?

It's all in the title. To be more complete, the following is stated in the preamble of the Wikipedia article about S-duality: One of the earliest known examples of S-duality in quantum field theory ...
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23 views

Explicitly determining the propagator for the dual field

So I have a question which has been on my mind for some time but I never got around to asking: how can I calculate the propagator for a dual field? Let me go into some more detail. Starting off with ...
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126 views

T-duality rules between D-branes and E-branes

I am trying to understand the time-like T-duality rules in Type II effective actions, and how they relate D-branes to E-branes. In the case of the metric and dilaton, the Buscher rules are unchanged ...
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1answer
126 views

Why is the electromagnetic duality an S-duality?

One of the examples that Wikipedia gives of S-duality is the EM duality. Namely that $$ \begin{align} \mathbf{E} &\rightarrow\mathbf{B} \\ \mathbf{B} &\rightarrow -\frac{1}{c^2}\mathbf{E} \...
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Does there exist a duality between the following two quantum systems?

Consider two systems: A) $N$ number of independent spin $0$ bosons living on a circle. B) A single spin $0$ boson moving on an $N$-torus. How do we detect the difference between the two systems ...
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What's the symmetry group $SU(N)/Z_N$?

I'm trying to understand David Tong's notes, specifically the discussion around page 92 where he's arguing that a different symmetry group may the group of QCD, namely $G'=SU(N)/Z_N$ instead of $G=SU(...
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115 views

Why is the Jordan-Wigner transformation an example of an S-duality?

The Jordan-Wigner transformation allows one to map a spin theory to a fermionic theory and, according to wikipedia, it is an example of an S-duality. In turn, according to the wiki page for the S-...
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1answer
98 views

Kramers-Wannier duality high and low temperature expansions confusion

I am reading the section on the 2D Ising model Krammer-Wannier duality in the book Exactly Solved Models in Statistical Mechanics (pg. ~76) by R.J. Baxter. I have two questions: What was the ...
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186 views

Deriving conserved charges from the equations of motion

It is very well established how to derive conserved charges associated to the symmetries of Lagrangian using the Noether's theorem. Also in the Hamiltonian formulation, we know how to derive the ...
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One-loop exactness of self-dual Yang-Mills theory

The self-dual Yang-Mills theory (gauge group $G$) with the action: $$ \mathcal{S} = \int_{M} \text{Tr} (B^{+} \wedge F) $$ where $B^{+}$ is a self-dual field, transforming in the adjoint ...
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1answer
116 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 ...
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Anomalies in the self-dual Yang-Mills theory and $\mathcal{N}=2$ open-string theory

I am reading a paper, written by G. Chalmers and W. Siegel - https://arxiv.org/abs/hep-th/9606061, where they discuss the action of self-dual Yang-Mills theory, which in light-cone formalism is ...
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1answer
157 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 ...
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1answer
60 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 ...
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1answer
160 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\...
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2answers
160 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 ...
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1answer
109 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'...
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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 ...
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2answers
116 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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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) ...
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47 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 ...
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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)...
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3answers
177 views

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

In Maxwell theory we have dual description in terms of dual fields: $$ \tilde{F}_{\mu\nu} = \partial_\mu \tilde{A}_\nu - \partial_\nu \tilde{A}_\mu = \varepsilon_{\mu\nu\rho\sigma} F^{\rho\sigma} $$ $...
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1answer
204 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 ...
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1answer
110 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 ...
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1answer
120 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 ...
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2answers
316 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 ...
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165 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(\...
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47 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 ...
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$T$-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.
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327 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 ...
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1answer
91 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?
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25 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. ...
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1answer
278 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
39 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 ...
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1answer
508 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
194 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 ...
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248 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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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 ...
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1answer
152 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 ...
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1answer
247 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 ...
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61 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
326 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\...