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Papers by Dan Xie
Journal of Physics A: Mathematical and Theoretical, 2014
In this paper we study the combinatorics associated with the positive orthogonal Grassmannian OG ... more 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 d log forms. Unlike N = 4 super Yang-Mills, here the Jacobian plays a crucial role to ensure the d log form of the reduced representation. Furthermore in the positive region, 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.
Journal of Physics A: Mathematical and Theoretical, 2014
In this paper we study the combinatorics associated with the positive orthogonal Grassmannian OG ... more 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 d log forms. Unlike N = 4 super Yang-Mills, here the Jacobian plays a crucial role to ensure the d log form of the reduced representation. Furthermore in the positive region, 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.