Related papers: Cardy Algebras, Sewing Constraints and String-Nets
The focusing theorem in General Relativity underlies causality, singularity theorems, entropy inequalities, and more. In AdS/CFT, we show that focusing in the bulk leads to a bound on CFT $n$-point functions that is generally stronger than…
We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a {\em tree algebra}. Using the Riemann-Hilbert correspondence, we…
This is an introductory survey on cluster algebras and their (additive) categorification using derived categories of Ginzburg algebras. After a gentle introduction to cluster combinatorics, we review important examples of coordinate rings…
In this paper we analyse the structure of the Cuntz semigroup of certain $C(X)$-algebras, for compact spaces of low dimension, that have no $\mathrm{K}_1$-obstruction in their fibres in a strong sense. The techniques developed yield…
The present paper deals with the question of representability of nets of C*-algebras whose underlying poset, indexing the net, is not upward directed. A particular class of nets, called C*-net bundles, is classified in terms of C*-dynamical…
We prove a spectral theorem for bimodules in the context of graph C*-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order) iff it is generated by the Cuntz-Krieger partial…
A recently proposed model of confining strings has a non-local world-sheet action induced by a space-time Kalb-Ramond tensor field. Here we show that, in the large-D approximation, an infinite set of ghost- and tachyon-free truncations of…
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…
This thesis investigates correspondences between open and closed strings. This is done on the level of coupled open-closed moduli spaces and from a string field theoretic point of view. The construction of boundary string field theory on…
We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing…
A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories,…
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…
This talk begins with some history and basic facts about string theory and its connections with strong interactions. Comparisons of stacks of Dirichlet branes with curved backgrounds produced by them are used to motivate the AdS/CFT…
We prove that the modular operad of diffeomorphism classes of Riemann surfaces with both `open' and `closed' boundary components, in the sense of string field theory, is the modular completion of its genus 0 part quotiented by the Cardy…
Elements of a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus $g$ are given. Sheaves of representations of affine Krichever-Novikov algebras over a dense open subset of the moduli space of Riemann…
A Cardy formula for 6d superconformal field theories (SCFTs) conjectured by Di Pietro and Komargodski in [1] governs the universal behavior of the supersymmetric partition function on $S^1_\beta \times S^5$ in the limit of small $\beta$ and…
We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary…
The algebraic approach to the Constraint Satisfaction Problem (CSP) uses high order symmetries of relational structures -- polymorphisms -- to study the complexity of the CSP. In this paper we further develop one of the methods the…
Let Q be a finite quiver without oriented cycles, and let $\Lambda$ be the corresponding preprojective algebra. Let g be the Kac-Moody Lie algebra with Cartan datum given by Q, and let W be its Weyl group. With w in W is associated a…
We establish rigid tensor category structure on finitely-generated weight modules for the subregular $W$-algebras of $\mathfrak{sl}_n$ at levels $ - n + \frac{n}{n+1}$ (the $\mathcal{B}_{n+1}$-algebras of Creutzig-Ridout-Wood) and at levels…