theories:speculative_theories:conformal_field_theory
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theories:speculative_theories:conformal_field_theory [2018/02/23 17:09] jakobadmin ↷ Page moved from theories:conformal_field_theory to theories:speculative_theories:conformal_field_theory |
theories:speculative_theories:conformal_field_theory [2018/03/26 15:10] jakobadmin |
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| ====== Conformal Field Theory ====== | ====== 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> | + | <tabbox Intuitive> |
| - | 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> | + | Conformal field theory is either a classical field theory or quantum field theory with only massless particles. In such theories, there is no mass scale and hence the theory is scale invariant, which means it looks the same no matter from how far away we look at it. |
| - | </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]] | + | |
| - | + | ||
| - | <tabbox Layman> | + | |
| - | + | ||
| - | <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. | + | |
| - | </note> | + | |
| | | ||
| - | <tabbox Student> | + | <tabbox Concrete> |
| <note tip> | <note tip> | ||
| Line 35: | Line 15: | ||
| </note> | </note> | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| <note tip> | <note tip> | ||
| Line 41: | Line 21: | ||
| </note> | </note> | ||
| - | --> Common Question 1# | + | <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> |
| - | --> Common Question 2# | + | <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> |
| - | | + | |
| - | <tabbox Examples> | + | |
| - | --> Example1# | ||
| - | + | <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.** |
| - | --> Example2:# | + | <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]] | |
| - | <-- | + | |
| - | + | ||
| - | <tabbox History> | + | |
| </tabbox> | </tabbox> | ||
theories/speculative_theories/conformal_field_theory.txt · Last modified: 2019/06/10 10:25 by jakobadmin
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