Related papers: Star-Product Functions in Higher-Spin Theory and L…
The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we…
We propose a hybrid class of theories for higher spin gravity and matrix models, i.e. which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev's higher spin gravity but part of the…
We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials…
New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields $B_{\mu\nu}$ and $C$, which was introduced in ArXiv:1304.7941[hep-th], is formulated. By using a local symmetry, two of the components of…
Higher-spin theory contains a complex coupling parameter $\eta$. Different higher-spin vertices are associated with different powers of $\eta$ and its complex conjugate $\bar \eta$. Using $Z$-dominance Lemma, that controls spin-locality of…
This short summary of recent developments in quantum compact groups and star products is divided into 2 parts. In the first one we recast star products in a more abstract form as deformations and review its recent developments. The second…
Many related products and coproducts (e.g. Hadamard, Cauchy, Kronecker, induction, internal, external, Solomon, composition, Malvenuto-Reutenauer, convolution, etc.) have been defined in the following objects : species, representations of…
Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and $(p_-(L),\, p_+(L))$ be the maximal interval of exponents $q\in[1,\,\infty]$ such that the semigroup…
A recently developed viewpoint on the fundamentals of density-functional theory for finite interacting spin-lattice systems that centers around the notion of degeneracy regions is presented. It allows for an entirely geometrical description…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation…
Generic solution of free equations for massless fields of an arbitrary spin in $AdS_4$ is built in terms of the star-product algebra with spinor generating elements. A class of "plane wave" solutions is described explicitly.
We describe a model of massive matter fields interacting through higher-spin gauge fields in 2+1 dimensional space-time. The two main conclusions are that the parameter of mass $M$ appears as a module characterizing an appropriate vacuum…
Recently, a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity - was given a covariant formulation both in flat and $(A)dS_4$ spacetimes at the level of equations of motion. We…
The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.
In this survey, we discuss two research areas related to Massey's higher operations. The first direction is connected with the cohomology of Lie algebras and the theory of representations. The second main theme is at the intersection of…
The formal algebraic structures that govern higher-spin theories within the unfolded approach turn out to be related to an extension of the Kontsevich Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one to…
It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain…
We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.
Properties of the resolution operator ${\rm d}_{loc}^*$ in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the…
We study continuous phase spaces of single spins and develop a complete description of their time evolution. The time evolution is completely specified by so-called star products. We explicitly determine these star products for general spin…