Related papers: Fusion Categories over Non-Algebraically Closed Fi…
We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. A quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge…
Pseudoscalar particles, with almost zero mass and very weak coupling to the visible matter, arise in many extensions of the standard model of particle physics. Their mixing with photons in the presence of an external magnetic field leads to…
Fusion is defined for arbitrary lowest weight representations of $W$-algebras, without assuming rationality. Explicit algorithms are given. A category of quasirational representations is defined and shown to be stable under fusion.…
We show that every fusion category containing a non-invertible, self-dual object $a$ gives rise to an integrable anyonic chain whose Hamiltonian density satisfies the Temperley-Lieb algebra. This spin chain arises by considering the…
In theories with extra dimensions there are generically brane kinetic terms for fields living in the bulk. These modify the masses and wave functions of the Kaluza-Klein expansions, and then the effective four dimensional gauge and Yukawa…
Interaction of branes in presence of internal gauge fields is considered by using the boundary state formalism. This approach enables us to consider the problems that are not easily accessible to the canonical approach via open strings. The…
"Fusion rules" are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras, in turn, are…
There have been many suggestions that there are extra spatial dimensions "outside" of our normal (3+1)-dimensional space. Generally it is assumed that electromagnetic and hadronic fields are restricted to the normal dimensions, while…
We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible co-dimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form…
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
We examine the contributions to rare processes that arise in models where the Standard Model fermions are localized at distinct points in compact extra dimensions. Tree-level flavor changing neutral current interactions for the Kaluza-Klein…
A $\gamma$-deformed version of $su(2)$ algebra with non-hermitian generators has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. The related Jordan-Schwinger(J-S) map is combined with boson algebras to obtain a hierarchy…
We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of $\R^n$ in a way that is completely algebraic.…
It was shown by Ostrik (2003) and Natale (2017) that a collection of twisted group algebras in a pointed fusion category serve as explicit Morita equivalence class representatives of indecomposable, separable algebras in such categories. We…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
It is offered that $F(R)-$modified gravities can be considered as nonperturbative quantum effects arising from Einstein gravity. It is assumed that nonperturbative quantum effects gives rise to the fact that the connection becomes…
Let $A$ be a simple algebra over a field $F$. Under a mild cardinality assumption on $F$, we determine the greatest possible dimension for an $F$-affine subspace of $A$ that is included in the group of units $A^\times$, and we describe the…
Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete…
This paper addresses the classification problem of associative algebras over arbitrary base fields. We present a list of three-dimensional associative algebras with canonical representatives of the isomorphism classes for fields of…
Manin triple construction of N=4 superconformal field theories is considered. The correspondence between quasi Frobenius finite-dimensional Lie algebras and N=4 superconformal field theories is established.