‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

A bstract We complete the proof of “Feynman rules” for constructing M -point conformal blocks with external and internal scalars in any topology arbitrary spacetime dimension by combining rules (based on their Witten diagram interpretation) construction cross ratios OPE “flow diagrams”). The full set Feynman leads to as power series hypergeometric type ratios. then provide a recursion which rel...

By extending the work published at ICCS 2020 [1], in this paper we propose a method to achieve cost-effective 3D printing of stiffened thin-shell objects. Our proposed consists three parts. The first part integrates finite element analysis, Voronoi diagram, and conformal mapping obtain stiffener distribution. second combines analysis with optimization calculations determine optimal sizes stiffe...

We present a general relation between celestial correlation functions in $d$-dimensions and Witten diagrams $\left(d+1\right)$-dimensional Euclidean anti-de Sitter (EAdS) space, to all orders perturbation theory. Contact diagram processes are proportional contact diagrams, particle exchanges can be recast as continuum of EAdS where the exchanged particles carrying unitary Principal Series repre...

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

A bstract We study two-dimensional string theory on a time-dependent background, whose worldsheet description consists of Liouville at central charge c = 1 and 25, together with the conformal ghosts. compute tree-level three-point four-point components cosmological wavefunction in perturbation theory. The latter is evaluated numerically by decomposing correlation functions into Virasoro blocks ...

A bstract The singlet sector of the O ( N ) ϕ 4 -model in AdS at large- , gives rise to a dual conformal field theory on boundary which is deformation generalized free field. We identify and compute an three-point one-loop fish diagram that controls exact dimensions operator product coefficients (OPE) for all “double trace” operators as function renormalized -couplings. find space -coupling com...

We continue the study of AdS loop amplitudes in spectral representation and position space. compute finite coupling 4-point function space for large-$N$ conformal Gross Neveu model on $AdS_3$. The resummation bubble diagrams gives a result proportional to tree-level contact diagram. show that certain families fermionic Witten can be easily computed from their companion scalar diagrams. Thus, ma...