Exclusion Inside or at the Border of Conformal Bootstrap Continent

TL;DR

This paper investigates the maximum possible anomalous dimensions in conformal field theories, demonstrating that the Pauli exclusion principle effectively saturates bootstrap bounds in two dimensions and approaches them in higher dimensions.

Contribution

It introduces a method using the Pauli exclusion principle to efficiently achieve large anomalous dimensions and compares its effectiveness across different dimensions.

Findings

In 2D, the method saturates the conformal bootstrap bound.

In higher dimensions, it nearly saturates the bound but may fall slightly inside.

The approach is most efficient in two dimensions.

Abstract

How large can anomalous dimensions be in conformal field theories? What can we do to attain larger values? One attempt to obtain large anomalous dimensions efficiently is to use the Pauli exclusion principle. Certain operators constructed out of constituent fermions cannot form bound states without introducing non-trivial excitations. To assess the efficiency of this mechanism, we compare them with the numerical conformal bootstrap bound as well as with other interacting field theory examples. In two dimensions, it turns out to be the most efficient: it saturates the bound and is located at the (second) kink. In higher dimensions, it more or less saturates the bound but it may be slightly inside.