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Cluster algebras and the subalgebra constructibility of the seven-particle remainder function

Abstract We review various aspects of cluster algebras and the ways in which they appear in the study of loop-level amplitudes in planar \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory. In particular, we highlight the different forms of cluster-algebraic structure that appear in this theory’s two-loop MHV amplitudes — considered as functions, symbols, and at the level of...

Making Visible the Invisible: The Role of Editing in Media Analysis and Language Arts

Arts John Golden 0 1 0 Portland Public Schools , Portland, OR , USA 1 Media Education Lab. Copyright and Fair Use. Temple University - Introduction we need to look at media products is to look closely

Mellin bootstrap for scalars in generic dimension

Abstract We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively...

USDA ARS Corn Breeding

. Disciplines Agricultural Science | Agriculture Authors Jode W. Edwards, Mike Blanco, John Golden, Fred Engstrom, Andrew Smelser, and Nuo Shen Thi s southeast research and demonstration farm is available at Iowa ... State University Digital Repository: farms_reports/273 RFR-A1074 Jode Edwards, research geneticist Mike Blanco, GEM coordinator John Golden, research technician Fred Engstrom

A cluster bootstrap for two-loop MHV amplitudes

We apply a bootstrap procedure to two-loop MHV amplitudes in planar \( \mathcal{N}=4 \) super-Yang-Mills theory. We argue that the mathematically most complicated part (the Λ2 B 2 coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure...

No unitary bootstrap for the fractal Ising model

We consider the conformal bootstrap for spacetime dimension 1 < d < 2. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed ϵ-expansion and Monte Carlo simulations of the Ising model on fractal lattices. The bounds clearly rule out that these models correspond to unitary conformal field...

An analytic result for the two-loop seven-point MHV amplitude in \( \mathcal{N} \) = 4 SYM

Abstract We describe a general algorithm which builds on several pieces of data available in the literature to construct explicit analytic formulas for two-loop MHV amplitudes in \( \mathcal{N} \) = 4 super-Yang-Mills theory. The non-classical part of an amplitude is built from A 3 cluster polylogarithm functions; classical polylogarithms with (negative) cluster \( \mathcal{X...

The differential of all two-loop MHV amplitudes in \( \mathcal{N}=4 \) Yang-Mills theory

We present an explicit analytic calculation of the differential of the planar n-particle, two-loop MHV scattering amplitude in \( \mathcal{N}=4 \) super Yang-Mills theory. The result is expressed only in terms of the polylogarithm functions Li k (−x), for k = 1, 2, 3, with arguments x belonging to the special class of dual conformal cross-ratios known as cluster \( \mathcal{X...