PIRSA:12110049 Scientific Series Quantum Fields and Strings

DOI10.48660/12110049

Series: Quantum Fields and Strings

Paulos, M. (2012). Bootstrapping CFTs with the Extremal Functional Method. Perimeter Institute. https://pirsa.org/12110049

Paulos, Miguel. Bootstrapping CFTs with the Extremal Functional Method. Perimeter Institute, Nov. 27, 2012, https://pirsa.org/12110049 

@misc{ pirsa_PIRSA:12110049,
  doi = {10.48660/12110049},
  url = {https://pirsa.org/12110049},
  author = {Paulos, Miguel},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Bootstrapping CFTs with the Extremal Functional Method},
  publisher = {Perimeter Institute},
  year = {2012},
  month = {nov},
  note = {PIRSA:12110049 see, \url{https://pirsa.org}}
}

Abstract

The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the allowed region the extremal functional contains, in principle, enough information to determine the dimensions and OPE coefficients of an infinite number of operators appearing in the correlator under analysis. Based on this idea we develop the Extremal Functional Method (EFM), a numerical procedure for deriving the spectrum and OPE coefficients of CFTs lying on the boundary (of solution space). We test the EFM by using it to rederive the low lying spectrum and OPE coefficients of the 2d Ising model based solely on the dimension of a single scalar quasi-primary -- no Virasoro algebra required. Our work serves as a benchmark for applications to more interesting, less known CFTs in the near future, such as the 3d Ising model.

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