Related papers: A Conformal Dispersion Relation: Correlations from…
We study a statistical model defined by a conformally invariant distribution of overlapping spheres in arbitrary dimension d. The model arises as the asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space, and also as…
We show that if the permittivity profile of a planar dielectric medium is an analytic function in the upper (lower) half complex position plane then it won't reflect radiation from the left (right), whatever the angle of incidence.…
We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on…
Cosmological correlation functions are significantly more complex than their flat-space analogues, such as tree-level scattering amplitudes. While these amplitudes have simple analytic structure and clear factorisation properties,…
In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis.…
The behavior of a strongly charged polymer adsorbed on an oppositely charged surface of low-dielectric constant is formulated by the functional integral method. By separating the translational, conformational, and fluctuational degrees of…
We extend Kramers-Kronig relations beyond the optical approximation to dielectric functions that depend not only on frequency but on the wave number as well. This implies extending the notion of causality commonly used in the theory of…
A seemingly obvious extension of the weak equivalence principle, in which all matter must respond to Post-Newtonian gravitational fields, such as Lense-Thirring and radiation fields, in a composition-independent way, is considered in light…
To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are…
These lecture notes give a pedagogical introduction to the use of dispersion relations in loop calculations. We first derive dispersion relations which allow us to recover the real part of a physical amplitude from the knowledge of its…
We derive explicit expressions for the conformal blocks of the Ising conformal field theory, for the correlators of an arbitrary number of primary fields. These results are obtained from the bosonized description of the Ising model.…
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 consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios $u,v$ interchange. This representation has several features in…
We introduce a formalism for conformal field theory in four dimensions: a symplectic bi-Grassmannian representation of CFT$_4$ Wightman correlators. Working in Klein space with off-shell spinor-helicity variables, we show that correlators…
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…
We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system…
We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule dispersive if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have…
The inference of causal relationships among observed variables is a pivotal, longstanding problem in the scientific community. An intuitive method for quantifying these causal links involves examining the response of one variable to…
We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of…
We review the relation between four-dimensional global conformal blocks and field propagation in ${\rm AdS_5}$. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar…