Cubic Representations of Open-String Effective Action Contact Terms and BCJ Relations at Four-Point One-Loop

Sammanfattning: The tree amplitudes of string theory low-energy effective actions admit a diagrammatic expansion in terms of higher-than-cubic contact terms. These tree amplitudes can be used to build loop amplitudes using unitary cuts or the forward limit. In this thesis we study the possibility of constructing four-point cubic representations for the resulting one-loop contact terms that obey the Bern-Carrasco-Johansson (BCJ) color-kinematics relation. From the string theory effective action we study the contact terms carrying ζ2, ζ3, ζ4, and ζ5. For the even ζ2 and ζ4 cases we find that the cubic representations are incompatible with the BCJ relations, as expected from their disappearance in the closed-string effective action. We find a unique, local set of numerators at ζ3 that obey the BCJ relations. For ζ5 we find two choices of representations: one obeys BCJ but requires non-trivial contributions for the tadpole; the other contains no tadpoles but breaks one of the BCJ relations.