One-loop diagrams with quadratic propagators from the worldsheet

Abstract

It is well known that forward limits of tree-level amplitudes (and those trivalent diagrams they consist of) produce one-loop amplitudes and trivalent diagrams with propagators linear in the loop momentum. They naturally arise from one-loop worldsheet formulae, and an important open problem is how to recombine them into usual one-loop diagrams with quadratic propagators. In this paper, we study a new collection of worldsheet functions: generalized one-loop Parke-Taylor factors with tensor numerators, which are conjectured to serve as a basis for one-loop worldsheet functions with this nice property. We present all-multiplicity, closed-form expressions for combinations of one-loop trivalent diagrams with quadratic propagators and tensor numerators to arbitrary rank (including possible tadpole contributions), produced by any pair of Parke-Taylor factors. We also briefly comment on reducing worldsheet functions onto such a basis, and applications to one-loop amplitudes in physical theories.

arXiv comment27+11 pages,2 figures; minor changes, clarifications added, published version

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• Perfecting one-loop BCJ numerators in SYM and supergravity
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• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Advanced tools for basis decompositions of genus-one string integrals
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories