✎ Conformal Field Theory [The Physics Travel Guide]

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====== Conformal Field Theory ======

<tabbox Why is it interesting?> 
<blockquote>
It is an old idea in particle physics that, in some sense, at sufficiently high energies the masses of the elementary particles should become unimportant. In recent years this somewhat vague hope has acquired a more definite form in the theory of scale transformations, or dilatations.

<cite>Aspects of Symmetry: Selected Erice Lectures by Sidney Coleman</cite>
</blockquote>

<blockquote>
In particle physics, one longstanding hope has been that at high energies, particle masses can be neglected, so that the physics would become scale invariant. It turns out that in a local field theory, it is true, more or less in general, that scale invariance typically leads to conformal invariance. (This is because the violation of scale invariance and conformal invariance are both determined by the trace $T^\mu_\mu$ of the energy momentum tensor.)

<cite>page 621 Einstein Gravity in a Nutshell - A. Zee</cite>
</blockquote>

<blockquote>
It seems that all QFTs can be viewed as points along an Renormalization Flow (or RG flow, this is the name we give to the zooming process) from a ‘UV’ CFT to another ‘IR’ CFT. Renormalization flows occur when we deform the UV CFT, breaking its conformal symmetry. [...] Well-defined QFTs can be viewed as either CFTs or as RG flows between CFTs. We can remove the UV cutoff from a QFT (send it to infinite energy or zero length) if it can be interpreted as an RG flow from the vicinity of a CFT fixed point. **So studying the space of CFTs basically amounts to studying the space of all well-defined QFTs.**

<cite>[[https://web.archive.org/web/20150616082629/http://www.pha.jhu.edu/~jaredk/AdSCFTCourseNotesPublic.pdf|Lectures on AdS/CFT from the Bottom Up]] by Jared Kaplan</cite>
</blockquote>

See also: https://www.quantamagazine.org/using-the-bootstrap-physicists-uncover-geometry-of-theory-space-20170223 and [[advanced_notions:critical_exponent|Critical Exponents]]

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
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<tabbox Student>

<note tip>
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
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<tabbox Researcher>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

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