Related papers: On Some Conformally Invariant Operators in Euclide…
We study twist operators in higher dimensional CFT's. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in…
In this paper, we study the perturbative aspects of a twisted version of the two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
Using polarization spinor methods in conjunction with the superspace formalism, we construct 3-point superconformal invariants that are used to determine the form of 3-point correlators of spinning superfield operators in $\mathcal{N}=1$…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
In this paper, we introduce an inverse problem of a Schr\"odinger type variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, for $0<s<1$. We determine the unknown bounded potential $q$ from the exterior partial…
We analyse the 3-point CFT correlators involving non-conserved spinning operators in momentum space. We derive a general expression for the conformal Ward identities defining the 3-point functions involving two generic spin $s$…
In this thesis are presented two aplications of the sigma model for the superstring in the pure spinor formulation. The first aplication concerns the computation of the one-loop conformal invariance for the type II superstring, resulting in…
On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler…
In this paper we study spectral properties of Schr\"odinger operators with quasi-periodic potentials related to quasi-periodic action minimizing trajectories for analytic twist maps. We prove that the spectrum contains a component of…
The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…
In a purely multi-variable setting (i.e., the issues discussed in this note are not interesting in the single variable operator theory setting), we show that the coincidence of two operator valued Schur class multipliers of a certain kind…
This article is concerned with the analysis of Dirac operators $D$ twisted by ramified Euclidean line bundles $(Z,\mathfrak{l})$-motivated by their relation with harmonic $\mathbf{Z}/2\mathbf{Z}$ spinors, which have appeared in various…
Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…
We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…
The nonlinearity of the conformal group is an essential factor that ruins the global conformal invariance for interacting material fields. In this paper we attempt to track such nonlinearity from spacetime transformations to spinor…
We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…
We consider deformations of CFTs from the perspective of parallel transport in moduli space. In particular, we show how the deformations of individual operators can be computed and we also explore how these ideas can be extended to more…
The main aims of this article are to characterize a class of operators associated with the symmetrized polydisc that admit rational dilations on the minimal space and to show an interplay between rational dilation and distinguished…
The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order differential operator preserving a space of wave…