Related papers: Self-similarity in cubic blocks of $\mathcal R$-op…
A phenomenon of "algebraic self-similarity" on 3d cubic lattice, providing what can be called an algebraic analogue of Kadanoff--Wilson theory, is shown to possess a 4d version as well. Namely, if there is a $4\times 4$ matrix $A$ whose…
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…
In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results…
The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solves Yang-Baxter equation. We build the R-operator as a product…
Discrete circular convolution over $\mathbb{Z}/N\mathbb{Z}$ is a linear operator and can be implemented on quantum hardware within the linear-combination-of-unitaries (LCU) framework. In this work, we make this connection explicit through…
We formulate a set of general rules for computing $d$-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed {\em off shell} with the Dirac,…
It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the…
The motivation of this paper is twofold. First, we investigate the block-diagonalization of the $z$-block circulant matrix $\mathtt{bcirc_z}(\mathcal A)$, based on this block-diagonal structure, and develop the algorithm…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks…
In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete…
In a space of $d=15 $ Grassmann coordinates, two types of generators of the Lorentz transformations, one of spinorial and the other of vectorial character, both linear operators in Grassmann space, forming the group $ SO(1,14) $ which…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in http://arxiv.org/abs/1602.01858 in several directions. First, we explicitly demonstrate that the action of quartic…