CFT Zoo

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list_of_cfts [2026/03/05 15:58]
Ludo Fraser-Taliente 		list_of_cfts [2026/03/19 00:09] (current)
Ludo Fraser-Taliente [List of CFTs]
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 Some special classes of CFTs: Some special classes of CFTs:
  
-  * [[tag:holographic]]+  * [[tag:holographic]] (also related to large-N CFTs)
   * [[tag:superconformal]]   * [[tag:superconformal]]
   * [[tag:logarithmic]]   * [[tag:logarithmic]]
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 ===== One dimension ===== ===== One dimension =====
  
-In 1d, the conformal Ward identity $T_\mu{}^\mu = 0$ implies $T_{00} = H = 0$. Therefore quantum systems which truly respect conformal invariance are non-local (see [[https://arxiv.org/pdf/1105.1772.pdf|here]] for another argument). Nonetheless, there are a number of interesting models exhibiting conformal symmetry or near conformal symmetry in one dimension.+In 1d, the conformal Ward identity $T_\mu{}^\mu = 0$ implies $T_{00} = H = 0$. Therefore quantum systems which truly respect conformal invariance are [[list_of_cfts#nonlocal_cfts|nonlocal]] (see [[https://arxiv.org/pdf/1105.1772.pdf|here]] for another argument). Nonetheless, there are a number of interesting models exhibiting conformal symmetry or near conformal symmetry in one dimension.
  
 {{topic>1d}} {{topic>1d}}
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 ===== Fractional/continuous dimension ===== ===== Fractional/continuous dimension =====
  
-Non-chiral CFTs can often be defined in continuous dimension $d$, though they are usually explicilty non-unitary for noninteger $d$ due to evanescent operators that have negative norm [[https://arxiv.org/abs/1512.00013 | 1]]. In the limit as $d$ approaches an integer, these evanescent operators decouple from the CFT.+Non-chiral CFTs can often be defined in continuous dimension $d$, though they are usually explicilty non-unitary for noninteger $d$ due to evanescent operators that have negative norm [[https://arxiv.org/abs/1512.00013 | 1]]. In the limit as $d$ approaches an integer, these evanescent operators decouple from the CFT. However, the unitarity can be hard to see from just the low-lying operators [[https://arxiv.org/pdf/2203.11597|1]].
  
 These CFTs apparently exist, even nonperturbatively. What's the conformal symmetry group? Possibly relevant: [[http://mr.crossref.org/iPage?doi=10.1070%2FRM1988v043n02ABEH001720]] These CFTs apparently exist, even nonperturbatively. What's the conformal symmetry group? Possibly relevant: [[http://mr.crossref.org/iPage?doi=10.1070%2FRM1988v043n02ABEH001720]]
Last modified: 2026/03/05 15:58
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