All Questions
Tagged with renormalization conformal-field-theory
92
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Conformal invariance and mass terms in QFT
We know that a physically sensible QFT must be renormalizable. If I understand correctly, when this happens, the theory has "asymptotic freedom" and is conformally invariant past some high ...
- 407
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59
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Can the Wilson-Fisher fixed point be reached from the massless $\phi^4$ action?
Most textbooks and papers work out the derivation of the Wilson-Fisher fixed point for $\phi^4$ starting from the massive action (in Euclidean space)
$$S = \int d^d x \biggl( \frac{1}{2} \partial_\mu \...
- 1,723
2
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58
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Distance conjecture being false in $\phi^4$ theory
One part of Distance conjecture states that free theory (Higher spin) are at infinite distance away from any arbitrary point on conformal manifold where the distance is measured with respect to ...
- 3,043
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Can a relevant operator's OPE with itself only include the identity and irrelevant operators?
I am interested in correlation functions in critical spin chains, and I'm trying to understand the consequences of conformal field theory for these correlation functions. I should warn that I do not ...
- 2,292
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84
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Conformal manifold of a supersymmetric field theory
I'm trying to understand what exactly is the conformal manifold of a theory. If I understand it right, the conformal manifold is the space of couplings.
From that point of view, it is just a subset ...
- 1,044
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54
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Beta function of CFT perturbed by several operators
As the title says, I am trying to derive the $\beta$ function of a CFT whose action is perturbed by several operators. The main refference I am following is https://arxiv.org/abs/1507.01960 starting ...
- 61
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102
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Beta function from renormalized coupling
While trying to derive a specific beta function for a CFT a stumbled upon the following. I have some bare coupling $g_b$ and introduce a renormalized coupling $g$ as
$$g_b=\mu^\epsilon(g+\frac{zg^2}{\...
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53
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$c$-theorem explicit examples
To give background, the $c$-theorem applies to 2D QFT's and the function form is given as $c(g) = C(g) + 4H + 6G$ where $C$, $H$ and $G$ are two point functions of the stress energy tensor.
So, I know ...
- 704
7
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327
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Does a CFT need a UV regulator?
I have a very basic question about conformal field theory: Does the partition function need a UV regulator, or is it finite even without? That is, does $\int D\phi \exp(-S)$ converge, or do we need to ...
- 1,455
6
votes
1
answer
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What Conformal Field theories are currently known to exist?
Conformal field theories (CFTs) pop up all over physics, especially in condensed matter and string theory. Their existence puts strong constraints on what quantum field theories can exist, since every ...
- 2,504
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(Renormalized) Stress Tensor in Di Francesco et al
in Chapter 5.2 regarding the Ward identities the authors introduce a renormalized energy-momentum tensor
$$T=-2\pi T_{zz}, \hspace{2cm} \bar{T}=-2\pi T_{\bar{z}\bar{z}}\hspace{2cm} (5.40)$$
What is ...
- 329
3
votes
1
answer
389
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Questions on RG flows, CFTs, and UV and IR theories
In the space of field theories, Conformal field theories are fixed points in the RG flow. However, a lot of literature on CFT usually talks about a QFT being the RG flow between two CFTs: one UV and ...
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-3
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187
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Is a running coupling constant a natural consequence in QFT, or is it a consequence of the "dressing-up" of particles?
The running coupling constant ("hold that constant!) is a well known phenomenon in quantum field theory. The constant varies with the energy of the interacting particles. I think this is rather ...
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How to show that in 2D CFT the marginal operator must have $(h,\bar h)=(1,1)$?
A related post might be
What are marginal fields in CFT?
where Qmechanic♦ pointed to Ginsparg secion 8.6.
However, I heard about two argument.
Claim 1:In a $D$ dimension CFT, the marginal operator ...
- 3,256
3
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240
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Examples of non-unitary CFT described by QFT fixed point
Are there examples of non-unitary CFTs that have a description in terms of some perturbative QFT approach in $d>2$? (I'd be happy with a bad one due to strong coupling.) Something like the epsilon ...
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