Topological Constraints on Defect Dynamics

TL;DR

This paper uncovers topological constraints on defect dynamics in quantum field theories, revealing how defect anomalies and symmetry reflecting defects impose robust, RG-invariant restrictions on defect behavior, supported by concrete examples.

Contribution

It introduces the concepts of defect anomalies and symmetry reflecting defects, providing a unified topological framework for understanding defect RG flows and related phenomena.

Findings

Defect anomalies are RG-invariant and encompass known and novel phenomena.

Symmetry reflecting defects remain coupled at low energies, constraining dynamics.

Concrete examples include exactly solvable defect RG flows in (1+1)d and a surface defect in (2+1)d scalar QED.

Abstract

Extended objects (defects) in Quantum Field Theory exhibit rich, nontrivial dynamics describing a variety of physical phenomena. These systems often involve strong coupling at long distances, where the bulk and defects interact, making analytical studies challenging. By carefully analyzing the behavior of bulk symmetries in the presence of defects, we uncover robust topological constraints on defect RG flows. Specifically, we introduce the notions of $\textit{defect anomalies}$ and $\textit{symmetry reflecting defects}$, both of which are RG-invariant. Several known notions, such as higher-form symmetries, fractionalization, and projective lines, are revealed to be manifestations of defect anomalies, which also encompass novel phenomena and forbid trivial defect dynamics in the IR. Meanwhile, symmetry reflecting defects are shown to remain coupled at low energies, imposing powerful dynamical constraints. We verify our findings through concrete examples: exactly solvable defect RG flows in (1+1)d Conformal Field Theories with symmetry reflecting lines and a surface defect in (2+1)d scalar QED.