Related papers: Clebsch (String) Parameterization of 3-Vectors and…
Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms…
The general method of reduction in the number of coupling parameters is applied in a Chern-Simons-matter model with several independent couplings. We claim that considering the asymptotic region, and expressing all dimensionless coupling…
We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. These can be viewed as Chern-Simons theories with special matter…
We classify the 3-point functions of local gauge-invariant single-trace operators in the scalar sector of planar N=4 supersymmetric Yang-Mills involving at least one su(3) operator. In the case of two su(3) and one su(2) operators, the…
We develop a perturbative QCD factorization theorem which is compatible with effective field theory. The factorization involves three scales: an infrared cutoff of order $\Lambda_{\rm QCD}$, a hard scale of order the $B$ meson mass, and an…
We present the partition function of Chern-Simons theory with the exceptional gauge group on three-sphere in the form of a partition function of the refined closed topological string with relation $2\tau=g_s(1-b) $ between single K\"ahler…
The ``$D$'' matrices for all states of the two fundamental representations and octet are shown in the generalized Euler angle parameterization. The raising and lowering operators are given in terms of linear combinations of the left…
This paper provides a combinatorial dictionary between three sets of objects: Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and the irreducible modules of the affine Hecke algebra $H_n$ (for generic $q$). In particular, we…
A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d…
The `mechanization' is a procedure of replacing a scalar field in 1+1 dimensions with a piece-wise linear function, i.e. a finite graph consisting of $N$ joints (vertices) and straight segments (edges). As a result, the field theory is…
We apply the noncommutative fields method for gauge theory in three dimensions where the Chern-Simons term is generated in the three-dimensional electrodynamics. Under the same procedure, the Chern-Simons term is shown to be cancelled in…
We investigate critical $N$-component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalisation. Global and local renormalisation group flows are solved analytically in the…
Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This…
The off-shell vector-tensor multiplet is considered in an arbitrary background of N=2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the…
We introduce the ``skew apolarity lemma'' and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in {$\bigwedge^dV_{\mathbb{C}}$ with $d\leq 3$ and $\dim V_{\mathbb{C}} \leq 8$}. New algorithms to…
We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar fields. We describe by this approach to deformation the results obtained by Coll et al. in [1], where it is stated…
The gauge-invariant Chern-Simons-type Lorentz- and CPT-breaking term is here reassessed and a spin-projector method is adopted to account for the breaking (vector) parameter. Issues like causality, unitarity, spontaneous gauge-symmetry…
This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincar\'e equations that naturally includes…
This is the second part of a paper describing a new concept of separation of variables applied to the classical Clebsch integrable case. The quadratures obtained in Part I (also uploaded in arXiv.org) lead to a new type of the Abel map…
We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…