Conformal bootstrap in Mellin space from GG systems

TL;DR

This paper introduces a new Mellin space approach to the conformal bootstrap using Gauss-Grassmann systems, enabling more effective bounds on the spectrum of conformal field theories.

Contribution

It presents a novel scheme relating conformal blocks to GG systems, simplifying Mellin transforms in conformal bootstrap calculations.

Findings

Demonstrates the usefulness of the method for spectrum bounds

Provides a new analytical framework for conformal bootstrap in Mellin space

Connects conformal blocks to hypergeometric functions via GG systems

Abstract

A simple scheme to express the Mellin transform of $D$-dimensional Euclidean conformal bootstrap equation is presented by relating conformal blocks to a Gauss-Grassmann (GG) system due to Gelfand-Graev, associated to conformal integrals, which, in turn, are generalised hypergeometric functions. Usefulness of the expression for obtaining bounds on the spectrum of fields is demonstrated.