Related papers: Fusion Categories over Non-Algebraically Closed Fi…
It is well known that inclusion of torsion in the gravitational formalism, leads to four-fermion interactions. Although the coupling constant of this interaction is strongly suppressed in four dimensions, its value is enhanced in models…
We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be…
In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under…
We review the very stringent lower bounds on the string scale that arise from flavor considerations in models with intersecting branes. Despite the absence of a realistic flavor structure at tree level, flavor changing interactions induce a…
We consider a subclass of the class of group-theoretical fusion categories: To every finite group $G$ and subgroup $H$ one can associate the category of $G$-graded vector spaces with a two-sided $H$-action compatible with the grading. We…
We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius…
We show that the discrete anomaly constraints governing popular non-Abelian symmetries of use in (e.g.) flavoured, supersymmetric, and dark matter model building typically subdivide into two classes differentiated by the simple restrictions…
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a…
The dynamics of fermions on curved spacetime requires a spin connection, which contains a part called contorsion, an auxiliary field without dynamics but fully expressible in terms of the axial current density of fermions. Its effect is the…
We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields…
In this article, we define three new operations on ideals which generalize integral closure and Frobenius closure of ideals, whose definitions incorporate an auxiliary ideal and a real parameter. These additional ingredients are common in…
We use the equations of motion in combination with crossing symmetry to constrain the properties of interacting fermionic boundary conformal field theories. This combination is an efficient way of determining operator product expansion…
In this talk, I discuss recent developments concerning the possibility of large extra spacetime dimensions. After briefly reviewing how such dimensions can lower the fundamental GUT, Planck, and string scales, I then outline how these…
We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between…
Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we…
It is well known that there exists a significant equivalence between the vector space $\mathbb{F}_{q}^n$ and the finite fields $\mathbb{F}_{q^n}$, and many scholars often view them as the same in most contexts. However, the precise…
A discussion of the influence of boundaries and scalar field interactions in the non-perturbative dynamics of fermions in an external magnetic field, along with their possible applications to condensed matter and cosmology, is briefly…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
This paper studies unbounded PAC fields and shows an amalgamation result for types over algebraically closed sets. It discusses various applications, for instance that omega-free PAC fields have the property NSOP3. It also contains a…
All independent interaction vertices involving massless (Fang--Fronsdal) fermions in three dimensions are classified, completing the classification of interactions of massless fields of any spin. Similarly to the bosonic case, we get no…