Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions

TL;DR

This paper introduces a nonlinear sigma model with a Wess-Zumino-Witten term as a universal framework for describing deconfined quantum critical points across arbitrary dimensions, emphasizing symmetry defect intertwinement.

Contribution

It generalizes the NLSM with WZW term to arbitrary dimensions and specifies the target space as a homogeneous space, providing a new theoretical approach to deconfined quantum criticality.

Findings

Proposes a universal NLSM framework for DQCP in any dimension.

Identifies the target space as a homogeneous space G/K for symmetry analysis.

Constructs models with Grassmannian defects in 3+1d and relates to fermionic models.

Abstract

In this paper, we propose using the nonlinear sigma model (NLSM) with the Wess-Zumino-Witten (WZW) term as a general description of deconfined quantum critical points that separate two spontaneously symmetry-breaking (SSB) phases in arbitrary dimensions. In particular, we discuss the suitable choice of the target space of the NLSM, which is in general the homogeneous space $G/K$, where $G$ is the UV symmetry and $K$ is generated by $\mathfrak{k}=\mathfrak{h}_1\cap \mathfrak{h}_2$, and $\mathfrak{h}_i$ is the Lie algebra of the unbroken symmetry in each SSB phase. With this specific target space, the symmetry defects in both SSB phases are on equal footing, and their intertwinement is captured by the WZW term. The DQCP transition is then tuned by proliferating the symmetry defects. By coupling the $G/K$ NLSM with the WZW term to the background gauge field, the 't Hooft anomaly of this theory can be determined. The bulk symmetry-protected topological (SPT) phase that cancels the anomaly is described by the relative Chern-Simons term. We construct and discuss a series of models with Grassmannian symmetry defects in 3+1d. We also provide the fermionic model that reproduces the $G/K$ NLSM with the WZW term.