PIRSA:18020081

Analytic conformal bootstrap in 1D

Mazac, D. (2018). Analytic conformal bootstrap in 1D. Perimeter Institute. https://pirsa.org/18020081

Mazac, Dalimil. Analytic conformal bootstrap in 1D. Perimeter Institute, Feb. 13, 2018, https://pirsa.org/18020081 

          @misc{ pirsa_PIRSA:18020081,
            doi = {10.48660/18020081},
            url = {https://pirsa.org/18020081},
            author = {Mazac, Dalimil},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Analytic conformal bootstrap in 1D},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {feb},
            note = {PIRSA:18020081 see, \url{https://pirsa.org}}
          }

Dalimil Mazac

CEA Saclay

Talk number
PIRSA:18020081
Collection
Talk Type
Subject
Abstract

All physical constraints of the conformal bootstrap in principle arise by applying linear functionals to the conformal bootstrap equation. An important goal of the bootstrap program is to identify a suitable basis for the space of functionals -- one that would allow us to solve crossing analytically. In my talk, I will describe two particularly convenient choices of the basis for the 1D conformal bootstrap. The two bases manifest the crossing symmetry of the four-point function of a generalized free boson and generalized free fermion respectively. I will use the bases to study small deformations of the two theories. Assuming no new operators appear in the OPE, the generalized free fermion allows no small deformation, and the generalized free boson allows a one-parameter deformation, which coincides with the AdS_2 four-point contact interaction at the leading order. Time allowing, I will discuss the connection of this work to the conformal bootstrap a la Polyakov.