Questions tagged [duality]

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AdS-CFT correspondance from 1D to 4D

From what I understand the AdS-CFT correspondence states that the bulk dynamics of a $n$-dimensional gravitational theory are encoded in the degrees of freedom of its dual CFT in the $(n-1)$ ...
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-2 votes
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52 views

Is superstring (M-theory) an effective theory from higher spin theory?

In the proceedings of the 2003 conference to celebrate Stephen Hawking's 60th birthday Hawking writes: String theorists have long used the term, effective theory, as a pejorative description of ...
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Duality between topological order and SPT in $K$-matrix formalism

It is a well-known fact that the low energy effective theory of intrinsic topological order is multi-components Chern-Simons theory $\frac{K_{I J}}{4 \pi} \int_{\mathcal{M}} d t d^{2} x \epsilon^{\mu \...
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10 votes
4 answers
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Why does gravity seem to have two natures (force or warping of space and time)?

In classical mechanics, gravity is regarded as a force but in general relativity it's a warping of space and time in presence of mass. Are these two definitions the same? Or is this a duality nature ...
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2 votes
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Are dualities necessarily quantum mechanical?

What happens to dualities in a certain limit where quantum mechanics is turned off? Like sending $\hbar/S$ $\rightarrow0$ where $S$ is the action of each side of the duality. Does the duality have a ...
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3 votes
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Quantized periods in electromagnetic duality path integral

In John McGreevy's notes (page 64 of https://mcgreevy.physics.ucsd.edu/w21/2021W-239-lectures.pdf), he describes a path integral derivation of electromagnetic duality for $p$-form gauge fields. The ...
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2 votes
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How to identify the dyon being condensated at the ${\cal N}=2$ SUSY $u$-plane?

For the $u$-plane monodromy at $u=u_0$ $$\mathcal{M}^{p,q}=\begin{pmatrix} 1+pq & p^2 \\ -q^2 & 1-pq \\ \end{pmatrix}$$ the statement is that dyons with electric and magnetic charges $(p,q)$ ...
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Why $T$-transformation is a symmetry in $d=4$ pure Maxwell theory?

The Maxwell $\theta$-term $\mathcal{S}_{\theta}=\int d^4x\frac{i\theta}{32\pi^2}\epsilon_{\mu\nu\rho\lambda}F^{\mu\nu}F^{\rho\lambda}$ has the identification for theories have $\theta$ and $\theta + 2\...
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Photon propagators in self-dual electromagnetism

$\quad$Consider extending Maxwell electromagnetism with the dual photon field $\tilde{A}$. The complex combinations $A^\pm = \frac{1}{2}(A \pm i\tilde{A})$ then serve as the potentials of the self-...
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Implications of M-Theory on the correctness of String Theory

So we know that there are 5 types of string theories (Type 1, Type IIA, Type IIB, $SO(32)$ heterotic, and $E_8 \times E_8$ heterotic). It was shown that these 5 types are just limits of something ...
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Isn't AdS/CFT an end to String theory as a fundamental theory?

I start with the Large $N$ QCD paper by 't Hooft. When 't Hooft published his paper on Large $N$ QCD it was clear why the string theory of hadrons due to Gabriele Veneziano could make sense. But at ...
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How can holographic duals (eg. AdS/CFT) be used to study magnetic monopoles? [closed]

What useful things are possible to find out about magnetic monopoles through the use of dual theories? I'm thinking of characteristics such as stability (or chaoticness), expectation values, central ...
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Brane fluctuations via $S$-duality

Caveat lector: I'm a mathematician trying to learn physics so I apologize if my questions are very vague or trivial. I'm currently studying Maldacena's Black Holes in String Theory (https://arxiv.org/...
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At the critical point, is Kramers-Wannier duality a unitary symmetry of the model?

I have in mind the transverse ising model and its (self-dual) generalizations, such as $$H_{TI} = \sum_i \sigma^z_{i}\sigma^z_{i+1} + h \sigma^x_{i}$$ and $$H_{SDANNI} = \sum_i (\sigma^z_{i}\sigma^z_{...
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Identical OPE behaviour of CFT of T-dual $X’^{\mu}$ of $X^{\mu}$

In chapter $8$ (String theory vol $\mathrm{I}$) sec $8.3$ Polchinski states that The field $X’^{25}$ has same OPE and energy momentum tensor as $X^{25}$ the minus signs always entering in pair $$X^{...
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14 votes
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Compact or non-compact boson from bosonization?

In some discussions of bosonization, it is stressed that the duality between free bosons and free fermions requires the use of a compact boson. For example, in a review article by Senechal, the ...
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1 answer
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What would happen if the fine structure constant were set to 1?

While reading up on magnetic monopoles, I have been led to understand that, due to S-duality, the magnetic equivalent of the fine-structure constant, $\alpha_M$ must be related to the reciprocal of $\...
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2 votes
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If magnetic monopoles existed, would the electric field also require a vector potential? [duplicate]

I'm studying magnetic duality and it seems that duality is nearly complete for the exception of the apparent non-existence of magnetic monopoles. My issue here isn't this one. My issue is that, if ...
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Action in AdS/CFT correspondence

I am a beginner trying to study AdS/CFT correspondence. Could someone please explain, can we connect action in the gravity side to the field theory side by this correspondence? Can we write the ...
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0 votes
1 answer
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Particle-antiparticle duality and special relativity

I was reading through Zee's QFT in a Nutshell and I reached the end of the second chapter, where Zee discusses the similarities between Compton scattering and electron-positron annihilation. While I ...
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1 answer
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Some questions about the compact boson in David Tong's notes on Gauge Theory

The notes can be found at http://www.damtp.cam.ac.uk/user/tong/gaugetheory.html. In Sec. 7.5.1, T-Duality, around Eq. 7.51, it says that the Bianchi identity $\partial_\mu(\epsilon^{\mu\nu}\partial_\...
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How do we perform a perturbative expansion for magnetic monopoles?

Magnetic monopoles in non-abelian (and even abelian) gauge theory essentially appear as a non-perturbative, composite phenomenon if we perform the standard perturbative expansion in terms of, say, ...
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1 vote
1 answer
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The Heisenberg model using the duality analysis

I would like to express the Heisenberg model using the duality analysis. It is shown here how to express the Ising model using Pauli matrices but I cannot get the relation $ \sigma _{i}^{z}= \prod_{...
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1 vote
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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?
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4 votes
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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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3 votes
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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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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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5 votes
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$T$-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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4 votes
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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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4 votes
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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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5 votes
1 answer
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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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1 vote
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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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6 votes
1 answer
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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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2 votes
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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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2 votes
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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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4 votes
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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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3 votes
1 answer
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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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3 votes
2 answers
283 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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5 votes
1 answer
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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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5 votes
1 answer
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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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3 votes
1 answer
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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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2 votes
1 answer
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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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8 votes
2 answers
176 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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2 votes
1 answer
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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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3 votes
2 answers
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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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3 votes
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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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2 votes
1 answer
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Free fermion dual to 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 proof ...
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