Related papers: String Diagrams for Physical Duoidal Categories

We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…

In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases…

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical…

It is well-known that combinatorial circuits are modeled mathematically by string diagrams in a monoidal category. Given a gate set $\Sigma$, the circuits over $\Sigma$ can be thought of as string diagrams in the free monoidal category…

Auxiliary string fields are introduced in light-cone gauge string field theory in order to express contact interactions as contractions of cubic vertices. The auxiliary field in the purely closed-string bosonic theory may be given a…

Classical diagram categories and monoids, including the Temperley--Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and admit additional twists that produce a large new family of…

We describe a 2-dimensional analogue of track categories, called two-track categories, and show that it can be used to model categories enriched in 2-type mapping spaces. We also define a Baues-Wirsching type cohomology theory for track…

We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…

The equations of motion of the massless sector of the two dimensional string theory, obtained by compactifying the heterotic string theory on an eight dimensional torus, is known to have an affine o(8,24) symmetry algebra generating an…

We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained…

We define bicategories internal to 2-categories. When the ambient 2-category is symmetric monoidal categories, this provides a convenient framework for encoding the structures of a symmetric monoidal 3-category. This framework is well…

String theory is the leading contemporary framework to explore the synthesis of quantum mechanics with gravity. String phenomenology aims to study string theory while maintaining contact with observational data. The fermionic $Z_2\times…

The aim of these notes is to give recent developments in string theory. In particular, we discuss the string spectrums, compactifications, brane physics and dualities.

We discuss a string-net construction on 2-framed surfaces, taking as algebraic input a finite, rigid tensor category, which is neither assumed to be pivotal nor semi-simple. It is shown that circle categories of our framed string-net…

We construct a space of string diagrams, which are a type of fatgraph with some additional data, and show that there are string topology operations on the chains of the free loop space of a closed Riemannian manifold which are parameterized…

We consider a conformal system of a string and a particle defined in D=10+2 space-time dimensions. The extra time-like dimension is a gauge artifact and can be eliminated by choosing a gauge in which the SO(10,1) Lorentz symmetry is…

We examine the structure of spacetime symmetries of toroidally compactified string theory within the framework of noncommutative geometry. Following a proposal of Frohlich and Gawedzki, we describe the noncommutative string spacetime using…

We give a pedagogical introduction to string theory, D-branes and p-brane solutions.

We give a brief summary of algebraic aspects of string theory arising in the noncommutative geometry setting of foliations called string diagrammatics which we introduced jointly with Bob Penner. We furthermore discuss how this gives rise…

We develop a systematic framework for understanding symmetries in topological phases in 2+1 dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon species and global symmetries permuting anyon species,…