Related papers: Unifying Constructions of Non-Invertible Symmetrie…
In recent years we have learned that several four-dimensional field theories can manifest non-invertible zero-form symmetries generalizing the Kramers-Wannier duality defect of the 2d critical Ising model. Several recent works by various…
We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point functions and the lasso two-point functions are derived,…
We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible…
We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a…
We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…
Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs). We discuss how to construct symmetries of QFTs by extending minimal "seed" symmetry groups to larger groups that contain the seed(s)…
Non-invertible symmetries have been extensively studied in quantum field theories in recent years. In this note we initiate their study in supergravity. We find infinite families of non-invertible defects in 11d and 10d Type II…
In recent years, the traditional notion of symmetry in quantum theory was expanded to so-called generalised or categorical symmetries, which, unlike ordinary group symmetries, may be non-invertible. This appears to be at odds with Wigner's…
We present practical and formal methods for gauging non-invertible symmetries in (2+1)d topological quantum field theories. Along the way, we generalize various aspects of invertible 0-form gauging, including symmetry fractionalization,…
Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized…
Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
We provide a lightning review of the construction of (generalised) orbifolds [arXiv:0909.5013, arXiv:1210.6363] of two-dimensional quantum field theories in terms of topological defects, along the lines of [arXiv:1307.3141]. This universal…
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…
Generalized symmetries of quantum field theories can be characterized by topological defects/operators organized into a higher category. In this paper we consider the Axion-Maxwell field theory in four dimensions and, building on the…
We survey recent developments in a novel kind of generalized global symmetry, the non-invertible symmetry, in diverse spacetime dimensions. We start with several different but related constructions of the non-invertible Kramers-Wannier…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
We summarize basic features of quantum field theories with discrete symmetry $\mathbb{Q}/\mathbb{Z}$ (possibly higher form, global or gauged). The classification of representations and anomalies is quite rich and involves the ring of…
We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
We describe the construction of theta summable and finitely summable spectral triples associated to Mumford curves and some classes of higher dimensional buildings. The finitely summable case is constructed by considering the stabilization…