Related papers: Defects via Factorization Algebras
The factorization of amplitudes into hard, soft and collinear parts is known to be violated in situations where incoming particles are collinear to outgoing ones. This result was first derived by studying limits where non-collinear…
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices.…
We propose a novel approach to logic-based learning which generates assumption-based argumentation (ABA) frameworks from positive and negative examples, using a given background knowledge. These ABA frameworks can be mapped onto logic…
Factor analysis refers to a statistical model in which observed variables are conditionally independent given fewer hidden variables, known as factors, and all the random variables follow a multivariate normal distribution. The parameter…
The boundary contribution of an amplitude in the BCFW recursion relation can be considered as a form factor involving boundary operator and unshifted particles. At the tree-level, we show that by suitable construction of Lagrangian, one can…
We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in non-chiral bosonic topological orders in 2+1 dimensions. Based on physical considerations, we derive a formula…
A conformal field theory (CFT) in dimension $d\geq 3$ coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" $b$ that multiplies the Euler density in the defect's Weyl anomaly. For defect…
We discuss BF theories defined on manifolds with spatial boundaries. Variational arguments show that one needs to augment the usual action with a boundary term for specific types of boundary conditions. We also show how to use this…
Let F be a field complete for a real valuation. It is a standard result in valuation theory that a finite extension of F admits a valuation basis if and only if it is without defect. We show that even otherwise, one can construct bases in…
The defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields, whenever positive characteristic is involved. We continue the detailed study of defect…
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
The Julia-Toulouse mechanism is used to show that the topological Abelian BF term may be induced by the condensation of electric charges. As an application we discuss the subtle question of including consistently magnetic defects into the…
Dropout is a simple yet effective algorithm for regularizing neural networks by randomly dropping out units through Bernoulli multiplicative noise, and for some restricted problem classes, such as linear or logistic regression, several…
We discuss the so called gauge invariant quantization of anomalous gauge field theory, originally due to Faddeev and Shatashvili. It is pointed out that the further non invariance of relevant path integral measures poses a problem when one…
The quantum action principle of renormalisation theory is applied to the antibracket-antifield formalism for Hamiltonian systems. General results on the local BRST cohomology allow one to prove that the anomalies appear in the time…
The theory of $\tau$-factorizations on integral domains was developed by Anderson and Frazier. This theory characterized all the known factorizations and opened the opportunity to create new ones. It can be visualized as a restriction to…
We present explicit mathematical structures that allow for the reconstruction of the field content of a full local conformal field theory from its boundary fields. Our framework is the one of modular tensor categories, without requiring…
We generalize the factorization method for inverse medium scattering using a particular factorization of the difference of two far field operators. Whilst the factorization method been used so far mainly to identify the shape of a…
Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended hamiltonian formalism can be used to define…