Related papers: Construction of Arbitrary Order Conformally Invari…
We construct quantum flux operators with respect to the Poincar\'e symmetry in the massless Dirac theory at future null infinity. An anomalous helicity flux operator emerges from the commutator of the superrotation generators. The helicity…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number…
Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the…
Cubic blocks are studied assembled from linear operators $\mathcal R$ acting in the tensor product of $d$ linear "spin" spaces. Such operator is associated with a linear transformation $A$ in a vector space over a field $F$ of a finite…
We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic…
We extend the results of arXiv:1401.1645 on the generalized conformal Sp(2n)-structure of infinite multiplets of higher spin fields, formulated in spaces with extra tensorial directions (hyperspaces), to the description of…
The semigroup of weighted composition operators $(W_n)_{n\in \mathbb{N}}$, defined by $$W_nf(z)=(1+z+\cdots +z^n)f(z^n),$$ acts on the classical Hardy-Hilbert space $H^{2}(\mathbb{D})$, and exhibits intriguing connections with both the…
We describe the equivariant cohomology of cofibers of spherical perverse sheaves on the affine Grassmannian of a reductive algebraic group in terms of the geometry of the Langlands dual group. In fact we give two equivalent descriptions:…
In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…
We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras $\mathcal{A}_b$ arising from a one-to-one correspondence between the sets of relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$ in…
Let ${\cal F}_\lambda$ be the space of tensor densities on ${\bf R}^n$ of degree $\lambda$ (or, equivalently, of conformal densities of degree $-\lambda{}n$) considered as a module over the Lie algebra $so(p+1,q+1)$. We classify…
We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these…
Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and…
The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using…
(Quasi)conformal scaling of composite operators from a strongly coupled EWSB dynamics helps to produce the characteristic hierarchies exhibited by the flavour couplings of the SM. It is however crucial to ensure that specific models satisfy…
We write a first order action for higher-spin fields and construct a canonical map to Fronsdal theory. The first-order description is defined over complex field configurations and has conformal invariance. We show that it is possible to…
Every four-dimensional ${\cal N}=2$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected…