Central Charge Bounds in 4D Conformal Field Theory

TL;DR

This paper establishes universal lower bounds on the stress tensor central charge in 4D conformal field theories based on crossing symmetry and operator dimensions, providing new constraints on CFT data.

Contribution

It introduces a model-independent method to bound the central charge using conformal bootstrap techniques and operator spectrum data.

Findings

Derived lower bounds on C_T based on scalar operator dimensions

Bound C_T universally using crossing symmetry constraints

Provides a new tool for constraining 4D CFTs

Abstract

We derive model-independent lower bounds on the stress tensor central charge C_T in terms of the operator content of a 4-dimensional Conformal Field Theory. More precisely, C_T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the CFT. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.