Related papers: Relative Anomalies in (2+1)D Symmetry Enriched Top…
One of the central ideas regarding anomalies in topological phases of matter is that they imply the existence of higher-dimensional physics, with an anomaly in a D-dimensional theory typically being cancelled by a bulk (D+1)-dimensional…
Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this paper we demonstrate how to compute…
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways , leading to a variety of symmetry enriched topological (SET) phases. While the symmetry…
We study anomalies in time-reversal ($\mathbb{Z}_2^T$) and $U(1)$ symmetric topological orders. In this context, an anomalous topological order is one that cannot be realized in a strictly $(2+1)$-D system but can be realized on the surface…
We study 't Hooft anomalies of symmetry-enriched rational conformal field theories (RCFT) in (1+1)d. Such anomalies determine whether a theory can be realized in a truly (1+1)d system with on-site symmetry, or on the edge of a (2+1)d…
We study a class of anomalies associated with time-reversal and spatial reflection symmetry in (2+1)D topological phases of matter. In these systems, the topological quantum numbers of the quasiparticles, such as the fusion rules and…
We classify symmetry fractionalization and anomalies in a (3+1)d U(1) gauge theory enriched by a global symmetry group $G$. We find that, in general, a symmetry-enrichment pattern is specified by 4 pieces of data: $\rho$, a map from $G$ to…
Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)$D$ on-site symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory to…
We study time-reversal symmetry in $(2+1)$D abelian bosonic topological phases. Time-reversal anomalies in such systems are classified by $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-protected topological (SPT) phases in $(3+1)$D, and can be…
We introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry enriched topological (SET) phases. We focus on bosonic systems with Z2 topological…
In a phase with fractional excitations, topological properties are enriched in the presence of global symmetry. In particular, fractional excitations can transform under symmetry in a fractionalized manner, resulting in different Symmetry…
We generalize the topological response theory to detect the boundary anomalies of linear subsystem symmetries. This approach allows us to distinguish different subsystem symmetry-protected topological (SSPT) phases and uncover new ones. We…
We study symmetry-enriched topological (SET) phases in 2+1 space-time dimensions with spatial reflection and/or time-reversal symmetries. We provide a systematic construction of a wide class of reflection and time-reversal SET phases in…
Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional…
We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a…
The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called…
Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group $G$, we show how to construct a (3+1)D topologically invariant path integral for a fermionic $G$ symmetry-protected topological…
We develop a theory of anomalies of fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general, $G_f$ can be a non-trivial central extension of the bosonic symmetry group $G_b$ by fermion…
Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture…
Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied…