Related papers: OPE in a generally covariant form
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index…
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…
We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a…
Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
There is a special set of massless four-dimensional gauge theories which admit local and gauge-anomaly-free uplifts to twistor space; we call such theories twistorial. In twistorial theories, generalized towers of soft modes (including…
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the…
We investigate the short-interval expansion of the subsystem fidelity in two-dimensional conformal field theories (2D CFTs) using the operator product expansion (OPE) of twist operators. We obtain universal contributions from general…
We introduce two notions of coarse embeddability between operator spaces: almost complete coarse embeddability of bounded subsets and spherically-complete coarse embeddability. We provide examples showing that these notions are strictly…
We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory. The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the…
We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a…
In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are "associativity" or "factorization" conditions on the operator product expansion (OPE) of…
Operator product expansion technique is analyzed in abelian and nonabelian nonsupersymmetric field theoretical models with confinement. Special attention is paid to the regimes where nonzero virtuality of vacuum fields is felt by external…
We consider the behavior of the OPE density $c(\Delta,\ell)$ for conformal four-point functions in the flat-space limit where all scaling dimensions become large. We find evidence that the density reduces to the partial waves $f_\ell(s)$ of…
Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_k (x_1, x_2) of dimension (k,k). For a {\it globally conformal invariant} (GCI) theory we write down…
The behavior under conformal change of the renormalized volume coefficients associated to a pseudo-Riemannian metric is investigated. It is shown that they define second order fully nonlinear operators in the conformal factor whose…
When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is…