Related papers: Categorical Anomaly Matching
We study the structure of anomalies in general heterotic string theories by considering general 2-dimensional $\mathcal{N}=(0,1)$ supersymmetric quantum field theories (SQFTs), without assuming conformal invariance nor the correct central…
Symmetry breaking of continuous symmetries by extended dynamical defects entails the existence of defect families, which form conformal manifolds in a critical setup. In the presence of bulk 't Hooft anomalies, defects are in fact required…
Anomaly detection to recognize unusual events in large scale systems in a time sensitive manner is critical in many industries, eg. bank fraud, enterprise systems, medical alerts, etc. Large-scale systems often grow in size and complexity…
Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including hyperspectral imaging, video surveillance and urban traffic monitoring. In the case of urban traffic data, anomalies refer…
We study non-abelian gauge theories with fermions in a representation such that the surviving electric 1-form symmetry is $\mathbb{Z}_2$. This includes $SU(N)$ gauge theories with matter in the (anti)symmetric and $N$ even, and $USp(2N)$…
Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular…
We consider general fermionic quantum field theories with a global finite group symmetry $G$, focusing on the case of 2-dimensions and torus spacetime. The modular transformation properties of the family of partition functions with…
We show that the 't Hooft anomaly of a quantum field theory with continuous flavor symmetry can be detected from rearrangements of the topological defect webs implementing the global symmetry in general spacetime dimension, which is…
Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms…
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…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
Quantum-inspired tensor networks algorithms have shown to be effective and efficient models for machine learning tasks, including anomaly detection. Here, we propose a highly parallelizable quantum-inspired approach which we call SMT-AD…
We address an anomaly detection setting in which training sequences are unavailable and anomalies are scored independently of temporal ordering. Current algorithms in anomaly detection are based on the classical density estimation approach…
In this paper, we systematically study gauge anomalies in bosonic and fermionic weak-coupling gauge theories with gauge group G (which can be continuous or discrete). We show a very close relation between gauge anomalies and…
Fusion category symmetries are finite symmetries in 1+1 dimensions described by unitary fusion categories. We classify 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry by using…
We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently…
We study the mixed 't Hooft anomaly of the subsystem symmetries in the exotic $BF$ theory and the foliated $BF$ theory in 2+1 dimensions, both of which are fractonic quantum field theories describing the equivalent physics. In the anomaly…
We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over rings of algebra integers. We show how to obtain TQFTs defined over algebra integers from these…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting…