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Boundary Witten effect in multi-axion insulators

Giandomenico Palumbo

TL;DR

This work generalizes axion electrodynamics to a framework with three dynamical axion fields, revealing new bulk topological defects and a boundary Witten-type effect. By performing a triple dimensional reduction from a $(6+1)$-D Chern-Simons theory, the authors derive a novel AX-EM coupling $S_{M\theta}$ that links three pseudoscalars to the electromagnetic field, and they connect this to a microscopic $(3+1)$-D Dirac model with three mass terms. In the bulk, suitable axion textures realize monopole-like configurations and Hopf solitons, while on a gapped boundary a $(2+1)$-D Witten effect emerges, giving vortices half-integer electric charge. These findings expand the landscape of topological phases and suggest new platforms for realizing and probing multi-axion physics in quantum materials and engineered systems, with potential extensions to non-Abelian, gravitational, and strain-induced axial phenomena.

Abstract

We explore novel topological responses and axion-like phenomena in three-dimensional insulating systems with spacetime-dependent mass terms encoding domain walls. Via a dimensional-reduction approach, we derive a new axion-electromagnetic coupling term involving three axion fields. This term yields a topological current in the bulk and, under specific conditions of the axions, real-space topological defects such as magnetic-like monopoles and hopfions. Moreover, once one the axions acquires a constant value, a nontrivial boundary theory realizes a (2+1)-dimensional analog of the Witten effect, which shows that point-like vortices on the gapped boundary of the system acquire half-integer electric charge. Our findings reveal rich topological structures emerging from multi-axion theories, suggesting new avenues in the study of topological phases and defects.

Boundary Witten effect in multi-axion insulators

TL;DR

This work generalizes axion electrodynamics to a framework with three dynamical axion fields, revealing new bulk topological defects and a boundary Witten-type effect. By performing a triple dimensional reduction from a -D Chern-Simons theory, the authors derive a novel AX-EM coupling that links three pseudoscalars to the electromagnetic field, and they connect this to a microscopic -D Dirac model with three mass terms. In the bulk, suitable axion textures realize monopole-like configurations and Hopf solitons, while on a gapped boundary a -D Witten effect emerges, giving vortices half-integer electric charge. These findings expand the landscape of topological phases and suggest new platforms for realizing and probing multi-axion physics in quantum materials and engineered systems, with potential extensions to non-Abelian, gravitational, and strain-induced axial phenomena.

Abstract

We explore novel topological responses and axion-like phenomena in three-dimensional insulating systems with spacetime-dependent mass terms encoding domain walls. Via a dimensional-reduction approach, we derive a new axion-electromagnetic coupling term involving three axion fields. This term yields a topological current in the bulk and, under specific conditions of the axions, real-space topological defects such as magnetic-like monopoles and hopfions. Moreover, once one the axions acquires a constant value, a nontrivial boundary theory realizes a (2+1)-dimensional analog of the Witten effect, which shows that point-like vortices on the gapped boundary of the system acquire half-integer electric charge. Our findings reveal rich topological structures emerging from multi-axion theories, suggesting new avenues in the study of topological phases and defects.

Paper Structure

This paper contains 5 sections, 39 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dimensional Reduction and Multi-Axion Terms
  3. Composite BF theory, monopoles and hopfions
  4. Boundary Witten effect and vortices
  5. Conclusion and Outlook

Figures (1)

  • Figure 1: Dimensional reduction of Chern-Simons theories (CS) that give rise to axion-electromagnetic coupling terms (AX-EM (n)). Here, n indicates the number of axion fields while the red arrows represent the dimensional reduction via compactification. Blu arrows refer to the relation between two theories once a single axion field acquires a constant value in the higher-dimensional theory such that the corresponding lower-dimensional action lives on the boundary of the parent theory via the Stokes' theorem. In this work, we mainly focus on the AX-EM theories coloured in green and yellow.