# Constructing Conformal Bootstrap Equations from the Embedding Space OPE Formalism

### APA

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

### MLA

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

### BibTex

@misc{ 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 Perimeter Institute

## 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