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J. M. Drummond - One of the best experts on this subject based on the ideXlab platform.

  • cluster adjacency properties of scattering amplitudes in n 4 supersymmetric yang mills theory
    Physical Review Letters, 2018
    Co-Authors: J. M. Drummond, Jack Foster, Omer Gurdogan
    Abstract:

    : We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study Heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.

  • A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
    Journal of High Energy Physics, 2015
    Co-Authors: J. M. Drummond, G. Papathanasiou, Marcus Spradlin
    Abstract:

    Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called Heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster $$ \mathcal{A} $$ -coordinates on Gr(4, 7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of Heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the 7 ∥ 6 collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the threeloop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n > 6.

  • A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
    Journal of High Energy Physics, 2015
    Co-Authors: J. M. Drummond, G. Papathanasiou, M. Spradlin
    Abstract:

    Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called Heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4,7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of Heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the $7 \parallel 6$ collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the three-loop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n>6.

M. Spradlin - One of the best experts on this subject based on the ideXlab platform.

  • A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
    Journal of High Energy Physics, 2015
    Co-Authors: J. M. Drummond, G. Papathanasiou, M. Spradlin
    Abstract:

    Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called Heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4,7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of Heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the $7 \parallel 6$ collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the three-loop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n>6.

Alexey A Popov - One of the best experts on this subject based on the ideXlab platform.

  • prato and bingel hirsch cycloaddition to Heptagon containing lasc2n cs hept c80 importance of pentalene units
    Chemical Communications, 2015
    Co-Authors: Qingming Deng, Alexey A Popov
    Abstract:

    Possible cycloaddition sites in the Heptagon-containing fullerene LaSc2N@Cs(hept)-C80 are studied computationally. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon (p/p) edges, whereas in the kinetically-controlled Bingel–Hirsch reaction the most reactive are carbons next to the p/p edge.

  • Synthesis and structure of LaSc2N@C(s)(hept)-C80 with one Heptagon and thirteen pentagons.
    Angewandte Chemie (International ed. in English), 2014
    Co-Authors: Yang Zhang, Kamran B Ghiassi, Qingming Deng, Nataliya A Samoylova, Marilyn M Olmstead, Alan L Balch, Alexey A Popov
    Abstract:

    The synthesis and single-crystal X-ray structural characterization of the first endohedral metallofullerene to contain a Heptagon in the carbon cage are reported. The carbon framework surrounding the planar LaSc2N unit in LaSc2N@C(s)(hept)-C80 consists of one Heptagon, 13 pentagons, and 28 hexagons. This cage is related to the most abundant Ih-C80 isomer by one Stone-Wales-like, Heptagon/pentagon to hexagon/hexagon realignment. DFT computations predict that LaSc2N@C(s)(hept)-C80 is more stable than LaSc2N@D5h-C80, and suggests that the low yield of the Heptagon-containing endohedral fullerene may be caused by kinetic factors.

  • Synthesis and Structure of LaSc2N@Cs(hept)‐C80 with One Heptagon and Thirteen Pentagons
    Angewandte Chemie, 2014
    Co-Authors: Yang Zhang, Kamran B Ghiassi, Qingming Deng, Nataliya A Samoylova, Marilyn M Olmstead, Alan L Balch, Alexey A Popov
    Abstract:

    The synthesis and single-crystal X-ray structural characterization of the first endohedral metallofullerene to contain a Heptagon in the carbon cage are reported. The carbon framework surrounding the planar LaSc2N unit in LaSc2N@Cs(hept)-C80 consists of one Heptagon, 13 pentagons, and 28 hexagons. This cage is related to the most abundant Ih- C80 isomer by one Stone-Wales-like, Heptagon/pentagon to hexagon/hexagon realignment. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, and suggests that the low yield of the Heptagon-containing endohedral fullerene may be caused by kinetic factors. According to the IUPAC definition, fullerenes are "Com- pounds composed solely of an even number of carbon atoms, which form a cage-like fused-ring polycyclic system with twelve five-membered rings and the rest six-membered rings", although the broadened definition also includes any closed cage structures consisting of three-coordinate carbon atoms. (1) The number of pentagons in this definition follows from Eulers theorem as applied to a polyhedron comprising only pentagons and hexagons. Furthermore, it was found that adjacent pentagons are strongly destabilizing, and hence the isolated pentagon rule (IPR) was formulated. (2) The IPR requires that each pentagon be surrounded by five hexagons and is rooted in the anti-aromaticity of the pentalene fragment and its high curvature, thus leading to the significant strain in an sp 2 -based carbon system.

  • synthesis and structure of lasc2n cs hept c80 with one Heptagon and thirteen pentagons
    Angewandte Chemie, 2014
    Co-Authors: Yang Zhang, Kamran B Ghiassi, Qingming Deng, Nataliya A Samoylova, Marilyn M Olmstead, Alan L Balch, Alexey A Popov
    Abstract:

    The synthesis and single-crystal X-ray structural characterization of the first endohedral metallofullerene to contain a Heptagon in the carbon cage are reported. The carbon framework surrounding the planar LaSc2N unit in LaSc2N@Cs(hept)-C80 consists of one Heptagon, 13 pentagons, and 28 hexagons. This cage is related to the most abundant Ih- C80 isomer by one Stone-Wales-like, Heptagon/pentagon to hexagon/hexagon realignment. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, and suggests that the low yield of the Heptagon-containing endohedral fullerene may be caused by kinetic factors. According to the IUPAC definition, fullerenes are "Com- pounds composed solely of an even number of carbon atoms, which form a cage-like fused-ring polycyclic system with twelve five-membered rings and the rest six-membered rings", although the broadened definition also includes any closed cage structures consisting of three-coordinate carbon atoms. (1) The number of pentagons in this definition follows from Eulers theorem as applied to a polyhedron comprising only pentagons and hexagons. Furthermore, it was found that adjacent pentagons are strongly destabilizing, and hence the isolated pentagon rule (IPR) was formulated. (2) The IPR requires that each pentagon be surrounded by five hexagons and is rooted in the anti-aromaticity of the pentalene fragment and its high curvature, thus leading to the significant strain in an sp 2 -based carbon system.

Volker Schomerus - One of the best experts on this subject based on the ideXlab platform.

  • The multi-Regge limit from the Wilson loop OPE
    Journal of High Energy Physics, 2020
    Co-Authors: Till Bargheer, Vsevolod Chestnov, Volker Schomerus
    Abstract:

    The finite remainder function for planar, color-ordered, maximally helicity violating scattering processes in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory possesses a non-vanishing multi-Regge limit that depends on the choice of a Mandelstam region. We analyze the combined multi-Regge collinear limit in all Mandelstam regions through an analytic continuation of the Wilson loop OPE. At leading order, the former is determined by the gluon excitation of the Gubser-Klebanov-Polyakov string. We illustrate the general procedure at the example of the Heptagon remainder function at two loops. In this case, the continuation of the leading order terms in the Wilson loop OPE suffices to determine the two-loop multi-Regge Heptagon functions in all Mandelstam regions from their symbols. The expressions we obtain are fully consistent with recent results by Del Duca et al.

Omer Gurdogan - One of the best experts on this subject based on the ideXlab platform.