Related papers: Universal Constraints for Conformal Line Defects
We propose a new class of universal amplitude ratios which involve the first terms of the short distance expansion of the correlators of a statistical model in the vicinity of a critical point. We will describe the critical system with a…
The covariant two-point functions, derived from Ward identities in direct space, can be affected by consistency problems and can become unbounded for large time- or space-separations. This difficulty arises for several extensions of…
Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as `conformal' transports and investigated over spaces with one affine connection and…
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…
Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the…
A necessary and sufficient condition on the precompactness of extremal sequences for one dimensional $\alpha$-Strichartz inequalities, equivalently $\alpha$-Fourier extension estimates, is established based on the profile decomposition…
This research focuses on trajectory planning problems for autonomous vehicles utilizing numerical optimal control techniques. The study reformulates the constrained optimization problem into a nonlinear programming problem, incorporating…
Recent years have seen growing interest in learning disentangled representations, in which distinct features, such as size or shape, are represented by distinct neurons. Quantifying the extent to which a given representation is disentangled…
We revisit the analysis of the integrated 2-point functions of local operators with a $\frac{1}{2}$-BPS Wilson line in $\mathcal{N}=4$ SYM. After including suitable parity-odd terms in the parametrization of the defect correlators, we are…
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…
We derive the system of equations that allows to include non-equilibrium correlations of filling numbers into the theory of the hopping transport. The system includes the correlations of arbitrary order in a universal way and can be cut at…
Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible…
Quasi-primary correlators in two-dimensional conformal field theories deformed simultaneously by $T\bar T$ and root-$T\bar T$ are studied. A path-integral formulation motivated by the geometric realization of the combined deformation is…
All four dimensional orbit spaces of compact coregular linear groups have been determined. The results are obtained through the integration of a universal differential equation, that only requires as input the number of elements of an…
General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…
We continue our study of the defect CFT on a Maldacena-Wilson line in N=4 Super-Yang-Mills theory using Bootstrability -- the conformal bootstrap supplemented with exact integrability data. In this paper, we extend this program to charged…
The study of quantum impurities has long been a central and inspiring theme in quantum many-body physics. Localized impurities are modeled by line defects in quantum field theory. We describe a line defect in Liouville CFT realized as a…
We study four-point correlators in superconformal theories in various dimensions. We develop an efficient method to solve the superconformal Ward identities in Mellin space. For 4d $\mathcal{N}=4$ SYM and the 6d $\mathcal{N}=(2,0)$ theory,…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with…