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Physical observables in the XY/sine-Gordon duality

My question is, during the duality map, real physical quantities seem to acquire a prefactor of $i$ and become purely imaginary. And I feel uncomfortable. Take bosonic current for example. Consider ...
T.P. Ho's user avatar
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2 votes
3 answers
56 views

What is the dual asymptotic spacetime of a CFT on a particular flat manifold?

According to AdS/CFT correspondence, the dual theory of a boundary CFT on flat spacetime is defined on an asymptotically AdS spacetime. The nature of the bulk spacetime depends on the topology of the ...
Sanjana's user avatar
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5 votes
0 answers
76 views

How many Lagrangians can a QFT have?

I just stumbled across a presentation by Tachikawa about "What is Quantum Field Theory". He has an interesting perspective that we should think of (at least a subset of) quantum field ...
11zaq's user avatar
  • 1,015
2 votes
2 answers
117 views

How to see that the Ising CFT has $c = 1/2$ while the quantum XY CFT has $c = 1$ via Jordan-Wigner?

It is well known that the CFT at the critical point of the 1+1d transverse field Ising model has central charge 1/2. This can be attributed to the fact that, after a Jordan-Wigner transformation, the ...
Midnight Conqueror's user avatar
1 vote
1 answer
80 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)(\...
daysofsnow's user avatar
1 vote
2 answers
108 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 ...
Spectree's user avatar
  • 227
5 votes
0 answers
84 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, ...
Lucas Queiroz's user avatar
4 votes
1 answer
151 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 ...
1 vote
0 answers
29 views

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 ...
Pratik Chatterjee's user avatar
5 votes
2 answers
443 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 ...
QFTheorist's user avatar
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0 answers
67 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_{...
Physics Koan's user avatar
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 ...
Zaza Orji's user avatar
  • 137
1 vote
0 answers
39 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
37 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 ...
Kai's user avatar
  • 3,710
2 votes
3 answers
361 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},$...
baba26's user avatar
  • 513
3 votes
1 answer
180 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 ...
dennis's user avatar
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2 votes
1 answer
103 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 ...
dennis's user avatar
  • 742
1 vote
3 answers
154 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 ...
ShoutOutAndCalculate's user avatar
2 votes
1 answer
83 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 ...
ShoutOutAndCalculate's user avatar
1 vote
1 answer
90 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 ...
Daniel T's user avatar
  • 113
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0 answers
34 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 ...
Burak Guner's user avatar
2 votes
1 answer
208 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 ...
John Eastmond's user avatar
5 votes
0 answers
199 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?
Loren's user avatar
  • 11
0 votes
1 answer
181 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 ...
Brian Bi's user avatar
  • 6,591
1 vote
2 answers
153 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} ...
Bastam Tajik's user avatar
  • 1,212
3 votes
0 answers
43 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?
J. H's user avatar
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2 votes
0 answers
76 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 ...
Kevin Marinas's user avatar
4 votes
1 answer
162 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_{...
Forum's user avatar
  • 87
1 vote
1 answer
138 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 $(n-1)$ ...
George Fanaras's user avatar
1 vote
0 answers
82 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 \...
GGBOND's user avatar
  • 11
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 ...
user134613's user avatar
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 ...
Bastam Tajik's user avatar
  • 1,212
3 votes
1 answer
189 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 ...
user321002's user avatar
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 $(p,q)$ ...
SSSSiwei's user avatar
  • 169
2 votes
0 answers
136 views

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-...
L-C's user avatar
  • 564
2 votes
1 answer
223 views

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 ...
The Gypsy King's user avatar
7 votes
1 answer
469 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 ...
Bastam Tajik's user avatar
  • 1,212
2 votes
0 answers
68 views

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 ...
Tim Hulland's user avatar
1 vote
0 answers
86 views

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/...
Rebour's user avatar
  • 145
6 votes
2 answers
1k views

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_{...
user196574's user avatar
  • 2,282
1 vote
0 answers
36 views

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^{...
aitfel's user avatar
  • 3,043
16 votes
2 answers
1k views

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 ...
Zack's user avatar
  • 3,088
2 votes
1 answer
170 views

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 $\...
Logan R. Kearsley's user avatar
2 votes
0 answers
35 views

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 ...
user2934303's user avatar
0 votes
0 answers
136 views

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 ...
QFT addict.'s user avatar
0 votes
1 answer
131 views

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 ...
Mirod the best's user avatar
1 vote
2 answers
337 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_\...
A.A.Lee's user avatar
  • 117
4 votes
0 answers
79 views

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, ...
Tevatron5's user avatar
1 vote
1 answer
141 views

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_{...
Rosa clara's user avatar

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