Related papers: Residual group-like symmetries in selection rules …
This work presents the conjugacy classes of finite abelian subgroups of the Cremona group of the plane. Using a well-known theory, this problem amounts to the study of automorphism groups of some Del Pezzo surfaces and conic bundles. We…
Various algebraic structures in geometry and group theory have appeared to be governed by certain universal rings. Examples include: the cohomology rings of Hilbert schemes of points on projective surfaces and quasi-projective surfaces; the…
The self-duality defects under discrete gauging in a categorical symmetry $\mathcal{C}$ can be classified by inequivalent ways of enriching the bulk SymTFT of $\mathcal{C}$ with $\mathbb{Z}_2$ 0-form symmetry. The resulting Symmetry…
We present a systematic study of non-supersymmetric type II toroidal asymmetric orbifolds with vanishing vacuum energy at one-loop in string perturbation theory. These are engineered through the conservation of a supercharge-like operator…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
This paper is a contribution to the study of the subgroup structure of exceptional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group $G$ is…
We consider the E8 x E8 heterotic string theory compactified on Calabi-Yau manifolds with bundles containing abelian factors in their structure group. Generic low energy consequences such as the generalised Green-Schwarz mechanism for the…
We study L-point couplings between twisted sector fields in heterotic orbifold compactifications, using conformal field theory. Selection rules provide an easy way to identify which couplings are non-vanishing. Those used in the current…
The goal of the present paper is to provide a detailed study of irreducible representations of the algebra generated by the symmetries of the generic quantum superintegrable system on the $d$-sphere. Appropriately normalized, the symmetry…
Fiber bundles over infinite fields with non-trivial ultra-norms are considered. For them geometric wrap groups are defined and investigated. Besides fields also Cayley-Dickson algebras over fields of characteristic not equal to two are…
We show that the category of abelian gerbes over a smooth manifold is equivalent to a certain category of principal bundles over the free loop space. These principal bundles are equipped with fusion products and are equivariant with respect…
This expository article presents a self-contained introduction to simplicial homology for finite simplicial complexes, emphasizing concrete computation and geometric intuition. Beginning with orientations of simplices and the construction…
Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated…
Finite symmetries abound in particle physics, from the weak doublets and generation triplets to the baryon octet and many others. These are usually studied by starting from a Lie group, and breaking the symmetry by choosing a particular…
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated…
A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group…
Motivated by recent progress in the spurion analysis of non-invertible selection rules (NISRs) arising from near-group fusion algebras, we further generalize the framework to a class of NISRs obtained from $\mathbb{Z}_2$ orbifolding of a…
In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form Rep(H) for H a suitable Hopf algebra (which includes the special…
We discuss the following proposition: Renormalization Group flow of quantum theory with a biased symmetry exhibits a fixed hypersurface at which the symmetry is exact. Such emergent symmetries may have important phenomenological…
The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every…