Related papers: Towards higher-spin holography in flat space
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…
The properties of the quantum Minkowski space algebra are discussed. Its irreducible representations with highest weight vectors are constructed and relations to other quantum algebras: $su_{q}(2)$, $q$-oscillator, $q$-sphere are pointed…
We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum…
In physics literature about supersymmetry, many authors refer to "super Minkowski spaces". These spaces are affine supermanifolds with certain distinguished spin structures. In these notes, we make the notion of such spin structures precise…
These notes provide a self-contained introduction to Lie algebroids, Lie-Rinehart algebras and their universal envelopes. This review is motivated by the speculation that higher-spin gauge symmetries should admit a natural formulation as…
We elaborate on various aspects of our top-down celestial holographic duality wherein the semiclassical bulk spacetime is a 4d asymptotically flat, self-dual K\"ahler geometry known as Burns space. The bulk theory includes an open string…
We formulate four dimensional higher spin gauge theories in spacetimes with signature (4-p,p) and nonvanishing cosmological constant. Among them are chiral models in Euclidean (4,0) and Kleinian (2,2) signature involving half-flat gauge…
It has been proposed that quantum mechanics and string theory share a common inner syntax, the relational logic of C. S. Peirce. Along this line of thought we consider the relations represented by spinors. Spinor composition leads to the…
We prove that an isometric immersion of a simply connected Riemannian surface M in four-dimensional Minkowski space, with given normal bundle E and given mean curvature vector H \in \Gamma(E), is equivalent to a normalized spinor field…
A Z3 symmetric generalization of the Dirac equation was proposed in recent series of papers, where its properties and solutions discussed. The generalized Dirac operator acts on "coloured spinors" composed out of six Pauli spinors,…
We consider the holographic duality between type-A higher-spin gravity in AdS_4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic…
Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is…
We consider Lie algebroids over algebraic spaces (in short we call it as $a$-spaces) by considering the sheaf of Lie-Rinehart algebras. We discuss about properties of universal enveloping algebroid $\mathscr{U}(\mathcal{O}_X,\mathcal{L})$…
A main purpose of this paper is to explain how the theory of higher spin fields in flat D=4 space and in AdS(4) emerges as a result of the quantization of a superparticle propagating in so called tensorial superspaces which have the…
Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral form. We also produce explicit commutation formulas…
We present a complete solution to the problem of Formal Higher Spin Gravities --- formally consistent field equations that gauge a given higher spin algebra and describe free higher spin fields upon linearization. The problem is shown to be…
Scalar QFT on the boundary $\Im^+$ at null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory is…
It is shown that the Schrodinger symmetry algebra of a free particle in d spatial dimensions can be embedded into a representation of the higher-spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry…
We consider two new classes of twisted D=4 quantum Poincar\'{e} symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincar\'{e} algebras which provide the…
Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the quantization of the algebra of functions on the…