Related papers: Edge contraction on dual ribbon graphs and 2D TQFT
We consider a one-parameter family of composite fields -- bi-linear in the components of the stress-energy tensor -- which generalise the $\mathrm{T}\bar{\mathrm{T}}$ operator to arbitrary space-time dimension $d\geq 2$. We show that they…
A digraph is 2-regular if every vertex has both indegree and outdegree two. We define an embedding of a 2-regular digraph to be a 2-cell embedding of the underlying graph in a closed surface with the added property that for every…
We use F-theory to classify possibly all six-dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F-theory (which correspond to allowed collections of…
We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the $\lambda T\bar T$ deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each…
This article concerns properties of mixed $\ell$-adic complexes on varieties over finite fields, related to the action of the Frobenius automorphism. We establish a fiberwise criterion for the semisimplicity and Frobenius semisimplicity of…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
We classify four-dimensional effective field theories (EFTs) with enhanced soft limits, which arise due to non-linearly realised symmetries on the Goldstone modes of such theories. We present an algorithm for deriving all possible algebras…
We introduce a family of dualities between certain non-supersymmetric self-dual gauge theories on a large class of $4d$ self-dual asymptotically flat backgrounds, and the large $N$ limit of an independently defined $2d$ chiral defect CFT.…
We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from…
The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissible covers. We study the asymptotic behavior of…
It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in…
In this brief sequel to a previous article, we recall the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cells. We…
It is shown that the four $(3 + 1)$-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory…
Delta lenses are functors equipped with a suitable choice of lifts, generalising the notion of split opfibration. In recent work, delta lenses were characterised as the right class of an algebraic weak factorisation system. In this paper,…
Let $\mathbb{k}$ be a characteristic zero domain. We define and study a diagrammatic monoidal $\mathbb{k}$-linear supercategory $\mathbf{Web}^{aff}_{A}$ associated to any locally unital Frobenius $\mathbb{k}$-superalgebra $A$. This category…
We explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras,…
Let $\Cc$ and $\Dd$ be two corings over a ring $A$ and $\Cc\stackrel{\lambda}{\longrightarrow}\Dd$ be a morphism of corings. We investigate the situation when the associated induced ("corestriction of scalars") functor…
We introduce a commutative associative graded algebra structure on the direct sum Z of the centers of the Hecke algebras associated to the symmetric groups in n letters for all n. As a natural deformation of the classical construction of…
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…
The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and…