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Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
We review some of the recent developments in the construction of $W$-string theories. These are generalisations of ordinary strings in which the two-dimensional ``worldsheet'' theory, instead of being a gauging of the Virasoro algebra, is a…
Representation theory, for the classical binary polyhedral groups is encoded by the affine Dynkin diagrams E6^{(1)}, E7^{(1)} and E8^{(1)} (McKay correspondance). The quantum versions of these classical geometries are associated with…
We point out that the moduli sector of the $(2,2)$ string compactification with its nonperturbatively preserved non-compact symmetries is a framework to study global topological defects. Based on the target space modular invariance of the…
By a conformal string in Euclidean space is meant a closed critical curve with non-constant conformal curvatures of the conformal arclength functional. We prove that (1) the set of conformal classes of conformal strings is in 1-1…
The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping…
Considering real spacetime as a Lorentzian fiber in a complex manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincar\'{e} groups. No spinors are allowed as linear…
The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…
String theory, specifically type-II superstring theory, can be formulated in any ten-dimensional signature. To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
W-algebras of finite type are certain finitely generated associative algebras closely related to the universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete…
In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions.…
There are many conceivable possibilities of embedding the MSSM in string theory. These proceedings describe an approach which is based on grand unification in higher dimensions. This allows one to obtain global string-derived models with…
We introduce and study the algebras of generalized quaternion type, which are natural generalizations of algebras which occurred in the study of blocks of group algebras with generalized quaternion defect groups. We prove that all these…
Assembly Theory, as developed by Cronin and co-workers, assigns to an object an assembly index: the minimal number of binary join operations required to build at least one copy of the object from a specified set of basic building blocks,…
In this note, we investigate the algebraic and topological representation theory of cylindric ortholattices and cylindric Boolean algebras. The first contribution demonstrates that cylindric ortholattices are closed under canonical…
We continue the exploration of various appearances of cluster algebras in scattering amplitudes and related topics in physics. The cluster configuration spaces generalize the familiar moduli space ${\mathcal M}_{0,n}$ to finite-type cluster…
A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries.…
On negatively curved compact manifolds, it is possible to associate to every closed form a bounded cocycle - hence a bounded cohomology class - via integration over straight simplices. The kernel of this map is contained in the space of…
In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by {\it Clifford cohomology.} We show that {\it Clifford…