1.4 GR as a QFT

[1]<ol><li>Qualls:2015qjb</li><li>Schellekens</li><li>Gillioz:2022yze</li><li>Blumenhagen:2009zz</li><li>Schottenloher:2008zz</li><li>Rychkov:2016iqz</li><li>davidsd</li><li>Nawata:2022lsw</li><li>Evans:2023iha</li><li>Frishman:2023fdk</li><li>Northe:2024tnm</li><li>Kusuki:2024gtq</li><li>Ginsparg:1988ui</li><li>Yin:2017yyn</li><li>Recknagel:2013uja</li></ol>. Main reference is [2]<ol><li>Nawata:2022lsw</li></ol>.\

I added supersymmetric CFT also in this section; maybe section susy should be before this section.

Reasons to study CFTs:

  1. The worldsheet descriptions of bosonic/superstring theories are 2D CFTs1.
  2. $D\geq 2$ CFTs are the holographic duals of superstring theories with $\geq 3$ noncompact dimensions.
  3. CFTs arise at fixed points of renormalization group flow. A generic point in the space of couplings corresponds to some general QFT at some energy scale described by some set of couplings. The properties of such a generic QFT are dictated largely by the fixed point because we can think of any QFT as a perturbation of a CFT by relevant operators. See Renormalizationgroupflow.
  4. Many areas of mathematics, such as vertex operator algebras, moduli spaces, low-dimensional topology, and geometric representation theory, have been influenced by CFTs.

Subsections

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  1. Strictly speaking, the worldsheet theory is a $2D$ quantum gravity since we some over topologies. CFT has a fixed manifold. ↩

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