Redundancy Channels in the Conformal Bootstrap

TL;DR

This paper introduces a method to prevent unintended symmetry enhancement in conformal bootstrap studies by identifying and constraining redundant operators, thereby improving the distinction between different symmetric theories.

Contribution

It develops a systematic approach to identify and utilize redundancy channels to differentiate theories with similar symmetries in conformal bootstrap calculations.

Findings

Identified a cubic redundancy channel in 3D models.

Demonstrated the method distinguishes cubic and O(3) models.

Established a new way to impose spectral gaps to control symmetry enhancement.

Abstract

A method for obstructing symmetry enhancement in numerical conformal bootstrap calculations is proposed. Symmetry enhancement refers to situations where bootstrap studies initialised with a certain symmetry end up allowing theories with higher symmetry. In such cases, it is shown that redundant operators in the less symmetric theory can descend from primary scaling operators of the more symmetric one, motivating the imposition of spectral gaps that are justified in the former but not the latter. The same mechanism can also be used to differentiate between decoupled and fully coupled theories which otherwise have the same global symmetry. A systematic understanding of this mechanism is developed and applied to distinguish the cubic from the $O(3)$ model in three dimensions, where a strip of disallowed parameter space, referred to as the cubic redundancy channel, emerges once a gap associated with a redundant operator of the cubic theory is imposed. The channel corresponds precisely to the region of parameter space where the assumed cubic symmetry would be enhanced to $O(3)$.