The positive orthogonal Grassmannian and loop amplitudes of ABJM
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Publication:2936563
DOI10.1088/1751-8113/47/47/474008zbMATH Open1307.81057arXiv1402.1479OpenAlexW2169335939WikidataQ59822188 ScholiaQ59822188MaRDI QIDQ2936563
Author name not available (Why is that?)
Publication date: 17 December 2014
Published in: (Search for Journal in Brave)
Abstract: In this paper we study the combinatorics associated with the positive orthogonal Grassmannian OG_k and its connection to ABJM scattering amplitudes. We present a canonical embedding of OG_k into the Grassmannian Gr(k,2k), from which we deduce the canonical volume form that is invariant under equivalence moves. Remarkably the canonical forms of all reducible graphs can be converted into irreducible ones with products of dLog forms. Unlike N=4 super Yang-Mills, here the Jacobian plays a crucial role to ensure the dLog form of the reduced representation. Furthermore, we identify the functional map that arises from the triangle equivalence move as a 3-string scattering S-matrix which satisfies the tetrahedron equations by Zamolodchikov, implying (2+1)-dimensional integrability. We study the solution to the BCFW recursion relation for loop amplitudes, and demonstrate the presence of all physical singularities as well as the absence of all spurious ones. The on-shell diagram solution to the loop recursion relation exhibits manifest two-site cyclic symmetry and reveals that, to all loop, four and six-point amplitudes only have logarithmic singularities.
Full work available at URL: https://arxiv.org/abs/1402.1479
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