Related papers: Formal Languages and TQFTs with Defects
This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two directions. First, we refine 2-dimensional cobordisms by…
We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/\Lambda \cong U(1)^n$ at level $K$, where $K:\Lambda\times\Lambda\to\mathbb Z$ is an even, integral, nondegenerate symmetric…
Integrality properties of partial sums over irreducible representations, along columns of character tables of finite groups, were recently derived using combinatorial topological string theories (CTST). These CTST were based on…
For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…
We study the Gram determinant and construct bases of hom spaces for the one-dimensional topological theory of decorated unoriented one-dimensional cobordisms, as recently defined by Khovanov, when the pair of generating functions is linear.
We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…
Term-forming operators (tfos), like iota- or epsilon-operator, are technical devices applied to build complex terms in formal languages. Although they are very useful in practice their theory is not well developed. In the paper we provide a…
In his PhD thesis, Goosen combined the string-net and the generators-and-relations formalisms for arbitrary once-extended 3-dimensional TQFTs. In this paper we work this out in detail for the simplest non-trivial example, where the…
The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…
We give an alternative presentation of Khovanov homology of links with strict functoriality result over integers. The construction uses an oriented $sl(2)$ state model allowing a natural definition of the boundary operator as twisted action…
The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect…
We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate…
Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…
First we define a unification grammar formalism called the Tree Homomorphic Feature Structure Grammar. It is based on Lexical Functional Grammar (LFG), but has a strong restriction on the syntax of the equations. We then show that this…
We propose an algebraic construction of the operator-state correspondence in non-relativistic conformal field theories by explicitly constructing an automorphism of the Schr\"odinger algebra relating generators in different frames. It is…
We construct a cohomology theory for oriented links using singular cobordisms and a special type of 2-dimensional Topological Quantum Field Theory (TQFT), categorifying the quantum sl(2) invariant. In particular, we give a description of…
An important open problem in geometric complex analysis is to find algorithms for explicit determination of basic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmuller and Grunsky norms,…
Conformal Quantum Field Theories (CFT) in 1 or 1+1 spacetime dimensions (respectively called chiral and full CFTs) admit several "axiomatic" (mathematically rigorous and model-independent) formulations. In this note, we deal with the von…
We study conformal defects in two important examples of string theory orbifolds. First, we show that topological defects in the language of Landau-Ginzburg models carry information about the RG flow between the non-compact orbifolds…
In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a…