Questions tagged [duality]
The duality tag has no usage guidance.
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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 ...
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3
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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 ...
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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 ...
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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 ...
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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)(\...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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
$$
dS^2_6 = dx^-dx^+ - \sum_{i,j=1}^4 A_{...
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Schrodinger's thought process about duality [duplicate]
How can a single particle be a wave?
Always thought wave is defined as back-and-forth motion for single particle, or we have many particles, wave should be as passing energy from one particle to ...
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Reference for dual gauge field and magnetic field being canonically conjugate
The gauge field operator in quantum Yang-Mills is canonically conjugate to the electric field.
I know that the dual gauge field is canonically conjugate to the magnetic field, but I can't seem to dig ...
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Superfluid-Maxwell duality and confinement in 3D
I learned in a class I took that there is a duality between a $D=3$ superfluid and $D=3$ Maxwell theory ($D$ being the dimension of spacetime). In the Euclidean formulation, the action of the ...
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Self-duality of Maxwell lagrangian in terms of magnetic gauge field
I have read at many places that the pure Maxwell theory (without any matter) is self-dual. This is the general form for Maxwell Lagrangian density:
$$\mathcal{L} = - \frac{1}{4} F_{\mu\nu} F^{\mu\nu},$...
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