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We revisit the problem of performing conformal block decomposition of exchange Witten diagrams in the crossed channel. Using properties of conformal blocks and Witten diagrams, we discover infinitely many linear relations among the crossed…
A method for constructing semianalytical strongly correlated wave functions for single and molecular quantum dots is presented. It employs a two-step approach of symmetry breaking at the Hartree-Fock level and of subsequent restoration of…
We consider maximal operators acting on vector valued functions, that is, functions taking values on $\mathbb{C}^d,$ that incorporate matrix weights in their definitions. We show vector valued estimates, in the sense of Fefferman--Stein…
We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We…
We study holographic defect conformal field theories which are dual to probe branes with bottom-up methods. First we determine the embedding of codimension-1 interface branes in AdS space. Then we compute defect one and two-point functions…
An extension of the AGT relation from two to three dimensions begins from connecting the theory on domain wall between some two S-dual SYM models with the 3d Chern-Simons theory. The simplest kind of such a relation would presumably connect…
The work describes the method of construction of charges (conserved quantities) for the gravity field in the (3 + 1) decomposition. The presented construction uses tensors of the electrical and magnetic parts of the Weyl tensor and…
This paper derives the CS decomposition for orthogonal tensors (T-CSD) and the generalized singular value decomposition for two tensors (T-GSVD) via the T-product. The structures of the two decompositions are analyzed in detail and are…
Many two-dimensional conformal field theories have an alternative integrable scattering description, which reproduces their spectrum of conformal weights. Taking as an example the case of the Lee-Yang nonunitary CFT and the 3-state Potts…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
We investigate the structure of join tensors, which may be regarded as the multivariable extension of lattice-theoretic join matrices. Explicit formulae for a polyadic decomposition (i.e., a linear combination of rank-1 tensors) and a…
In this paper we compute higher particle form factors of branch point twist fields. These fields were first described in the context of massive 1+1-dimensional integrable quantum field theories and their correlation functions are related to…
Gauge-Yukawa Unification (GYU) is a renormalization group invariant functional relation among gauge and Yukawa couplings which holds beyond the unification point in Grand Unified Theories (GUTs). Here, GYU is obtained by requiring…
We show how to obtain from highest weight representations of Krichever-Novikov algebras of affine type (also called higher genus affine Kac-Moody algebras) representations of centrally extended Krichever-Novikov vector field algebras via…
The construction of conformal blocks for the analysis of multipoint correlation functions with $N > 4$ local field insertions is an important open problem in higher dimensional conformal field theory. This is the first in a series of papers…
Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…
This paper explores a full generalization of the classical corner-vector method for constructing weighted spherical designs, which we call the {\it generalized corner-vector method}. First we establish a uniform upper bound for the degree…
We describe two crystal structures on set-valued decomposition tableaux. These provide the first examples of interesting "$K$-theoretic" crystals on shifted tableaux. Our first crystal is modeled on a similar construction of Monical,…
It has been argued that the Nekrasov's partition function gives the generating function of refined BPS state counting in the compactification of M theory on local Calabi-Yau spaces. We show that a refined version of the topological vertex…
The reaction of the elastic electron-deuteron scattering at high momentum transfer is investigated within the Bethe-Salpeter approach. The relativistic covariant Graz II separable kernel of nucleon-nucleon interactions is used to analyze…