Pinching rules in the chiral-splitting description of one-loop string amplitudes
| Autor: | Balli, Filippo Maria, Edison, Alex, Schlotterer, Oliver |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Loop amplitudes in string theories reduce to those of gauge theories and (super)gravity in their worldline description as the inverse string tension $\alpha'$ tends to zero. The appearance of reducible diagrams in these $\alpha' \rightarrow 0$ limits is determined through so-called pinching rules in the worldline literature. In this work, we extend these pinching rules to the chiral-splitting description of one-loop superstring amplitudes where left- and right-moving degrees of freedom decouple at fixed loop momentum. Starting from six points, the Kronecker-Eisenstein integrands of chiral amplitudes introduce subtleties into the pinching rules and integration-by-parts simplifications. Resolutions of these subtleties are presented and applied to produce a new superspace representation of the six-point one-loop amplitude of type IIA/B supergravity. The worldline computations and their subtleties are compared with the ambitwistor-string approach to one-loop field-theory amplitudes where integration-by-parts manipulations are shown to be more flexible. Throughout this work, the homology invariance of loop-momentum dependent correlation functions on the torus is highlighted as a consistency condition of $\alpha' \rightarrow 0$ limits and their comparison with ambitwistor methods. Comment: 56 + 20 pages; 1 Mathematica notebook added as an ancillary file which refers to lengthy data files available from https://doi.org/10.5281/zenodo.13992743 |
| Databáze: | arXiv |
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