On the Absence of Symmetric Simple Conformal Boundary Conditions

TL;DR

This paper investigates why certain 2D conformal field theories lack simple symmetric boundary conditions despite having trivial 't Hooft anomalies, revealing underlying reasons and proposing a diagnostic criterion using Symmetry TFT.

Contribution

It uncovers the reasons behind the absence of simple symmetric boundary conditions in specific CFTs and introduces a criterion to diagnose this failure based on Symmetry TFT analysis.

Findings

Counterexamples in tetracritical Ising and compact boson CFTs identified

A criterion for diagnosing the absence of boundary conditions proposed

Symmetry TFT plays a crucial role in understanding boundary conditions

Abstract

Non-trivial 't Hooft anomaly obstructs the existence of a simple symmetric conformal boundary condition in a CFT. Conversely, there is a common piece of lore that trivial 't Hooft anomaly promises the existence of a simple symmetry conformal boundary condition in a given CFT. Recently, counter examples to this lore was realized in tetracritical Ising CFT [1] and compact boson [2] -- the simple conformal boundary conditions preserving certain anomaly-free subsymmetry are absent in these CFTs. In this work, we uncover the underlying reason for the absence of these boundary conditions in counter examples, and propose a criterion diagnosing when the lore fails for any given 2d CFT. The Symmetry TFT description for boundary conditions plays a crucial role.