Questions tagged [duality]

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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 ...
1 vote
2 answers
306 views

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_\...
1 vote
2 answers
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Are dual bases and the Hodge dual "entirely distinct" uses of the word "dual", as per MTW?

NB: Basis one-forms and contravariant basis vectors (which, following Menzel, I am calling reciprocal) are the same thing. See, for example, the Mathematical Appendix to Gravitation and Inertia, by ...
1 vote
1 answer
65 views

Electromagnetic duality and vector/pseudovector transformation properties

One consequence of electromagnetic duality (see e.g., https://doi.org/10.1038/s41467-023-36420-4) is that if we have a system described by permittivity and permeability profile $(\varepsilon, \mu)(\...
15 votes
1 answer
754 views

Realization of: CFT generating function = AdS partition function

An important aspect of the AdS/CFT correspondence is the recipe to compute correlation functions of a boundary operator $\mathcal{O} $ in terms of the supergravity fields in the interior of the $AdS_{...
7 votes
1 answer
829 views

T-Duality between Type HE String theory and Type HO string theory

My question is regarding the T-Duality between the 2 Type H string theories. I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so $...
9 votes
2 answers
1k views

"$\theta$-$\phi$ duality" and $T$-duality -- is the free fermion theory self-dual?

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_\...
1 vote
2 answers
93 views

Why $N\to \infty$ limit implies $g_s \to 0$ in holographic QCD?

One basic difficulty in QCD is that it does not contain a small dimensionless quantity that would allow for perturbative calculation of low-energy observables. A remarkable feature of holographic ...
0 votes
4 answers
25k views

Relationship between Energy and Time [closed]

Is there a relationship between energy and time? What is it?
5 votes
0 answers
73 views

Question about the duality between 2+1 d transverse-field Ising model (TFIM) and $\mathbb{Z}_2$ gauge theory

I was reading McGreevy's Lecture notes Where do QFTs come from? , and on chapter 5 he talks about a duality between the $2+1d$ transverse-field Ising model (TFIM) and the $\mathbb{Z}_2$ gauge theory, ...
3 votes
0 answers
123 views

Derivation of self-dual gravity formulae

I am trying to read and understand this paper by Monteiro, Stark-Muchao, and Wikeley about self-dual yang-mills and self-dual gravity. In the introduction to this paper, they review a way to ...
5 votes
1 answer
230 views

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 ...
5 votes
2 answers
408 views

Is the self-dual point always a critical point?

I was studying duality maps in my Advanced Stat. Mech. class and it was told that all self-dual points need not correspond to critical point. I understand that critical points are points where ...
4 votes
1 answer
2k 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|^...
1 vote
0 answers
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Relation between curvature of spin connection, Weyl spinor and the cosmological constant

Consider the chiral version of Einstein-Cartan gravity. What is the relation between the self-dual part of the curvature of the spin connection $F^{AB}$, the cosmological constant $\Lambda$ and the ...
0 votes
0 answers
64 views

Solve Einstein equation with self-dual field strength

I have this action $$ S = \int d^6x \sqrt{g} \Big(R-\frac{1}{3}G_{\mu\nu\rho}G^{\mu\nu\rho}\Big) $$ on a $D=6$ dimensional manifold with the following metric $$ dS^2_6 = dx^-dx^+ - \sum_{i,j=1}^4 A_{...
74 votes
12 answers
18k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' ...
1 vote
0 answers
23 views

Schrodinger's thought process about duality [duplicate]

How can a single particle be a wave? Always thought wave is defined as back-and-forth motion for single particle, or we have many particles, wave should be as passing energy from one particle to ...
1 vote
0 answers
38 views

Reference for dual gauge field and magnetic field being canonically conjugate

The gauge field operator in quantum Yang-Mills is canonically conjugate to the electric field. I know that the dual gauge field is canonically conjugate to the magnetic field, but I can't seem to dig ...
2 votes
0 answers
33 views

Superfluid-Maxwell duality and confinement in 3D

I learned in a class I took that there is a duality between a $D=3$ superfluid and $D=3$ Maxwell theory ($D$ being the dimension of spacetime). In the Euclidean formulation, the action of the ...
2 votes
3 answers
313 views

Self-duality of Maxwell lagrangian in terms of magnetic gauge field

I have read at many places that the pure Maxwell theory (without any matter) is self-dual. This is the general form for Maxwell Lagrangian density: $$\mathcal{L} = - \frac{1}{4} F_{\mu\nu} F^{\mu\nu},$...
12 votes
0 answers
348 views

Intuition for Homological Mirror Symmetry

first of all, I need to confess my ignorance concerning physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand what ...
2 votes
1 answer
187 views

Is the Dirac monopole quantization condition out by 1/2?

Consider an electron with electric charge $e$ that is moved around a closed horizontal circular path $C$ centered around a magnetic monopole with magnetic charge $g$. Assume that the monopole produces ...
3 votes
1 answer
173 views

What does the dual gauge field have to do with topology?

The dual gauge field, $V$, is defined by $$^{\star}F(V)=F(A),$$ where $F$ is the field strength. The 't Hooft operator $\exp(i\int_C V)$ creates the trajectory of a magnetic particle along $C$. But I ...
2 votes
1 answer
98 views

What do monopoles have to do with strong coupling?

My understanding is that strong coupling effects arise from instantons in the path integral. But I sometimes read that monopoles (see the electric-magnetic duality) can allow one to calculate strong ...
39 votes
2 answers
11k views

What's the intuition behind the Choi-Jamiolkowski isomorphism?

What is the intuition behind the Choi-Jamiolkowski isomorphism? It says that with every superoperator $\mathbb{E}$ we can associate a state given by a density matrix $$ J(\mathbb{E}) = (\mathbb{E} \...
1 vote
3 answers
144 views

Are dualities symmetries? If so what are their conserved charges?

The dualities described the theories under certain transformations to be equivalent, i.e. $T$-duality described the equivalence between theories with $R$ and $\frac{1}{R}$. However, this looked very ...
2 votes
1 answer
71 views

How did the T-duality change the dimension of the $D$-brane?

Quote Clifford Johnson $D$-brane page 125 Observe that, since T-duality interchanges Neumann and Dirichlet boundary conditions, a further T-duality in a direction tangent to a $Dp$-brane reduces it ...
1 vote
1 answer
89 views

Are physical dualities based on mathematical dualities? [closed]

I understand what a physical duality is and what a mathematical duality is. The function to obtain the dual of an theory/object is an invertible function in both physics and math. I wonder if it is as ...
0 votes
0 answers
32 views

How is every D-brane dual to 2 others?

For instance, A D3 brane is T dual to both a D2 and D4. I understand the idea that Type A and B theories are T dual to one another, but I don't understand how you get 2 different dual descriptions ...
5 votes
0 answers
160 views

Reading list for JT/SYK correspondence

I have been studying Gábor Sárosi's review of holographic duality between Jackiw-Teitelboim gravity and the Sachdev-Ye-Kitaev models for the last few days. This field has grown since the review came ...
1 vote
0 answers
30 views

Regarding the single and double slit experiments

Are there interpretations of the single and double slit experiments, which discuss interactions between photons in transit, between the slits and the screen?
4 votes
1 answer
154 views

Why are we able to compare the open and closed string perspective in AdS/CFT?

I am reading the book Gauge/Gravity Duality Foundations and Applications by M. Ammon and J. Erdmenger. In that book they state the relationship between parameters on both sides of the duality as $$ g_{...
7 votes
1 answer
272 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 ...
0 votes
1 answer
163 views

Why can't the electromagnetic duality transformation be expressed in terms of potentials?

In Is it possible to elevate the electric-magnetic duality discrete symmetry to a continuous one? the OP asks about how to derive the Noether current associated with the electromagnetic duality ...
0 votes
2 answers
275 views

CFT energy scale in AdS/CFT correspondence

In the context of the AdS/CFT correspondence, the coordinate $z$ of AdS in Poincaré coordinates is often identified with an (inverse) energy scale for a CFT. I don't quite understand this ...
1 vote
2 answers
145 views

Is it possible to elevate the electric-magnetic duality discrete symmetry to a continuous one?

I'm familiar with Electric-Magnetic duality, where in the absence of source fields one can exchange the $F_{\mu \nu}$ field with the dual field: $\tilde{F}_{\mu \nu}={\epsilon}_{\mu \nu \alpha \beta} ...
3 votes
0 answers
42 views

Do all members of the affine Toda field theories have fermion duals?

I know that the sine-Gordon model is $S$-dual to the massive Thirring model. Since sine-Gordon is a special case of affine Toda theory I was wondering if this extends to the generality of the models?
2 votes
0 answers
71 views

Are we sure that electric “monopoles” are not just ends of an “Electrical Dirac String”? [closed]

The Dirac String is used to model magnetic monopoles. So how are we sure that physical electric “monopoles” are not in fact the ends of an “Electrical Dirac String” produced by a solenoid carrying a ...
1 vote
1 answer
120 views

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 $(n-1)$ ...
0 votes
1 answer
73 views

Shortest distance scales that a string can resolve

On page 5 of the notes by Veronika Hubeny on The AdS/CFT correspondence, we find the following: Nevertheless, already at this level we encounter several intriguing surprises. Since strings are ...
3 votes
1 answer
179 views

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 ...
1 vote
0 answers
75 views

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 \...
11 votes
4 answers
2k views

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 ...
6 votes
1 answer
276 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 ...
2 votes
0 answers
104 views

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 ...
7 votes
1 answer
437 views

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 ...
2 votes
0 answers
67 views

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 $(p,q)$ ...
2 votes
0 answers
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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-...
2 votes
1 answer
107 views

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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