Related papers: Symmetry of anomalous dimension matrices explained
It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for…
Quantum phase transitions in certain non-Hermitian systems controlled by non-tridiagonal Hamiltonian matrices are found anomalous. In contrast to the known models with tridiagonal-matrix structure in which the geometric multiplicity of the…
It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of maximal dimension if and only if they can be reduced…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
The noninvertible axial symmetry constructed from the ABJ-anomaly has attracted enormous interest. We discuss the mechanism of "symmetry-from-anomaly" in condensed matter-related models in both 1d and 3d spaces (which correspond to (1+1)d…
The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…
In this paper we consider anomalous dimensions of double trace operators at large spin ($\ell$) and large twist ($\tau$) in CFTs in arbitrary dimensions ($d\geq 3$). Using analytic conformal bootstrap methods, we show that the anomalous…
We construct accidentally symmetric potentials in the framework of Two Higgs Model Effective Field Theory (2HDMEFT) including higher-order operators of dimension 6 and dimension 8. Our construction is facilitated by an earlier developed…
This work is devoted to the proof of the statement about the existence of palindromic continued fractions in an arbitrary dimension. In addition, it is proved the criterion that an algebraic continued fraction has proper cyclic palindromic…
We discuss hidden symmetries of three-dimensional field configurations revealed at the one-particle level by the use of pseudoclassical particle models. We argue that at the quantum field theory level, these can be naturally explained in…
Two orthonormal bases B and B' of a d-dimensional complex inner-product space are called mutually unbiased if and only if |<b|b'>|^2=1/d holds for all b in B and b' in B'. The size of any set containing (pairwise) mutually unbiased bases of…
Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional…
In perturbation theory, the anomalous dimensions of twist-two operators have poles at negative or small positive integer values of spin and therefore must be resummed at these points. It was observed earlier that a certain quadratic…
We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as…
We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…
The set of badly approximable $m \times n $ matrices is known to have Hausdorff dimension $mn $. Each such matrix comes with its own approximation constant $c$, and one can ask for the dimension of the set of badly approximable matrices…
We consider the alternating sign matrices of the odd order that have some kind of central symmetry. Namely, we deal with matrices invariant under the half-turn, quarter-turn and flips in both diagonals. In all these cases, there are two…
Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
We study the isoperimetric problem for the radially symmetric measures. Applying the spherical symmetrization procedure and variational arguments we reduce this problem to a one-dimensional ODE of the second order. Solving numerically this…