PIRSA:22110103

Constructing Conformal Bootstrap Equations from the Embedding Space OPE Formalism

Prilepina, V. (2022). Constructing Conformal Bootstrap Equations from the Embedding Space OPE Formalism. Perimeter Institute. https://pirsa.org/22110103

Prilepina, Valentina. Constructing Conformal Bootstrap Equations from the Embedding Space OPE Formalism. Perimeter Institute, Nov. 18, 2022, https://pirsa.org/22110103 

          @misc{ pirsa_PIRSA:22110103,
            doi = {10.48660/22110103},
            url = {https://pirsa.org/22110103},
            author = {Prilepina, Valentina},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Constructing Conformal Bootstrap Equations from the Embedding Space OPE Formalism},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {nov},
            note = {PIRSA:22110103 see, \url{https://pirsa.org}}
          }

Valentina Prilepina

DOI 10.48660/22110103
Collection
Talk Type Scientific Series
Subject

Abstract

In this talk, I will describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced by Fortin and Skiba (DOI:10.1007/JHEP06(2020)028). To begin with, I will give some background on the formalism. In particular, I will map out how to build two-, three-, and four-point functions within this framework. I will then lay out how to construct tensorial generalizations of the well-known scalar four-point blocks for symmetric traceless exchange. As I will discuss, these generalized objects satisfy a number of contiguous relations. Together, these empower us to fully contract the four-point tensorial blocks, ultimately yielding finite spin-independent linear combinations of four-point scalar blocks potentially acted upon by first-order differential operators. I will next proceed to describe how to set up the conformal bootstrap equations directly in the embedding space. I will begin by mapping out a general strategy for counting the number of independent tensor structures, which leads to a simple path to generating the bootstrap equations. I will then examine how to implement this method to construct the two-point, three-point, and ultimately four-point conformal bootstrap equations. Lastly, I will illustrate this method in the context of a simple example.

Zoom link:  https://pitp.zoom.us/j/98920533892?pwd=cDQvOExJWnBsUWNpZml5S1cxb0FJQT09