160 research outputs found
S-matrix singularities and CFT correlation functions
In this note, we explore the correspondence between four-dimensional flat
space S-matrix and two-dimensional CFT proposed by Pasterski et al. We
demonstrate that the factorization singularities of an n-point cubic diagram
reproduces the AdS Witten diagrams if mass conservation is imposed at each
vertex. Such configuration arises naturally if we consider the 4-dimensional
S-matrix as a compactified massless 5-dimensional theory. This identification
allows us to rewrite the massless S-matrix in the CHY formulation, where the
factorization singularities are re-interpreted as factorization limits of a
Riemann sphere. In this light, the map is recast into a form of 2d/2d
correspondence.Comment: 18 page
True SYK or (con)sequences
Some generalizations of the Sachdev-Ye-Kitaev (SYK) model and different
patterns of their reparametrization symmetry breaking are discussed. The
analysis of such (pseudo)holographic systems relates their generalized
one-dimensional Schwarzian dynamics to (quasi) two-dimensional Liouvillian
quantum mechanics. As compared to the original SYK case, the latter might be
dissipative or have discrete states in its spectrum, either of which properties
alters thermodynamics and correlations while preserving the underlying
symmetry.Comment: Latex, no figure
High-Energy Amplitudes in Gauge Theories in the Next-to-Leading-Order
Scattering processes play a central role in physics, and high-energies experiments give us an insight into the fine structure of matter. The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (EIC) or Large Hadron electron Collider (LHeC)) one needs to know how large are the next-to-leading order (NLO) corrections. In addition, the NLO corrections define the scale of the running-coupling constant in the BK equation and therefore determine the magnitude of the leading-order cross sections. The first main result of this thesis is the calculation of these NLO corrections. In Quantum Chromodynamics (QCD), the next-to-leading order BK equation has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we first restore the conformal NLO BFKL kernel out of the eigenvalues known from the forward NLO BFKL result using the requirement of Möbius invariance of N=4 SYM amplitudes in the Regge limit, and then we calculate the NLO evolution of the color dipoles in the conformal N=4 SYM theory. To this end we define the composite dipole operator with the rapidity cutoff preserving conformal invariance, and the resulting Möbius invariant kernel for this operator agrees with the forward NLO BFKL calculation of Ref. [47]. In QCD, the NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling par
Fault-tolerance in metric dimension of boron nanotubes lattices
The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units not containing the faulty unit can replace the originally used chain is called a fault-tolerant self-stable system. Recent research studies reveal that the problem of finding metric dimension is NP-hard for general graphs and the problem of computing the exact values of fault-tolerant metric dimension seems to be even harder although some bounds can be computed rather easily. In this article, we compute closed formulas for the fault-tolerant metric dimension of lattices of two types of boron nanotubes, namely triangular and alpha boron. These lattices are formed by cutting the tubes vertically. We conclude that both tubes have constant fault tolerance metric dimension 4
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
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