Generalized Additivity in Unitary Conformal Field Theories

TL;DR

This paper generalizes bootstrap methods in 4D unitary conformal field theories to determine anomalous dimensions of all large spin operators, revealing a universal structure related to scalar operator dimensions.

Contribution

It extends previous bootstrap techniques to compute anomalous dimensions for all large spin operators, not just the leading ones, in 4D unitary CFTs.

Findings

Large spin operators have twists close to 2Δ+2N for scalar dimension Δ.

Generalized bootstrap methods apply to all large spin operators.

Operators correspond to excited states in AdS interpretations.

Abstract

It was demonstrated in recent work that $d=4$ unitary CFT's satisfy a special property: if a scalar operator with conformal dimension $\Delta$ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary operators have to exist in the operator spectrum of the CFT with a conformal twist close to $2\Delta+2N$ for any integer $N$. In this paper the conformal bootstrap methods that were used to find the anomalous dimension of the $N=0$ operators have been generalized to find the anomalous dimension of all large spin operators of this class. In AdS these operators can be interpreted as the excited states of the product states of objects that were found in other works.