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Title: CHY-graphs on a torus
Authors: Cardona, Carlos A.
Gomez, Humberto
Keywords: Differential and Algebraic Geometry;Field Theories in Higher Dimensions;Scattering Amplitudes
Issue Date: 12-Oct-2016
Publisher: Springer Verlag
Abstract: Recently, we proposed a new approach using a punctured Elliptic curve in the CHY framework in order to compute one-loop scattering amplitudes. In this note, we further develop this approach by introducing a set of connectors, which become the main ingredient to build integrands on M 1 , n , the moduli space of n-punctured Elliptic curves. As a particular application, we study the Φ 3 bi-adjoint scalar theory. We propose a set of rules to construct integrands on M 1 , n from Φ 3 integrands on M 0 , n , the moduli space of n-punctured spheres. We illustrate these rules by computing a variety of Φ 3 one-loop Feynman diagrams. Conversely, we also provide another set of rules to compute the corresponding CHY-integrand on M 1 , n by starting instead from a given Φ 3 one-loop Feynman diagram. In addition, our results can easily be extended to higher loops. © 2016, The Author(s).
ISSN: 11266708
Appears in Collections:Artículos Científicos

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