Related papers: String-net construction of RCFT correlators
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…
The Schwinger representation gives a systematic procedure for recasting large N field theory amplitudes as integrals over closed string moduli space. This procedure has recently been applied to a class of free field four point functions by…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
The Landau-Ginzburg/Conformal Field Theory correspondence predicts tensor equivalences between categories of matrix factorisations of certain polynomials and categories associated to the $N=2$ supersymmetric conformal field theories. We…
In this article we extend evaluations of the Kauffman bracket on regular isotopy classes of knots and links to a variety of functors defined on the category of framed tangles. We show that many such functors exist, and that they correspond…
We prove that the bundles with flat connections on configuration spaces associated to braided fusion categories, as well as the bundles with flat connections on moduli spaces of curves (conformal blocks) associated to modular fusion…
We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in hep-th/0504229.…
We show that all isomorphism classes of even rank Tambara-Yamagami categories arise as $\mathbb{Z}_2$-twisted representations of conformal nets. As a consequence, we show that their Drinfel'd centers are realized by (generalized) orbifolds…
A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric…
Let $\mathbb{k}$ be a commutative ring with global dimension zero. We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of $\mathbb{k}$. That is, the $\infty$-category of…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not…
Symmetry transformations of the space-time fields of string theory are generated by certain similarity transformations of the stress-tensor of the associated conformal field theories. This observation is complicated by the fact that, as we…
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…
The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a…
This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databases are models of theories in coherent…
We develop a purely combinatorial framework for the systematic enumeration of knot and link diagrams supported on the thickened torus $T^2\times I$. Using the theory of maps on surfaces, cellular $4$--regular torus projections are encoded…
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…
Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one…