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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.19641 |
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| _version_ | 1866910912313556992 |
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| author | Balli, Filippo Maria Edison, Alex Schlotterer, Oliver |
| author_facet | Balli, Filippo Maria Edison, Alex Schlotterer, Oliver |
| contents | Loop amplitudes in string theories reduce to those of gauge theories and (super)gravity in their worldline description as the inverse string tension $α'$ tends to zero. The appearance of reducible diagrams in these $α' \rightarrow 0$ 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 $α' \rightarrow 0$ limits and their comparison with ambitwistor methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19641 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pinching rules in the chiral-splitting description of one-loop string amplitudes Balli, Filippo Maria Edison, Alex Schlotterer, Oliver High Energy Physics - Theory Loop amplitudes in string theories reduce to those of gauge theories and (super)gravity in their worldline description as the inverse string tension $α'$ tends to zero. The appearance of reducible diagrams in these $α' \rightarrow 0$ 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 $α' \rightarrow 0$ limits and their comparison with ambitwistor methods. |
| title | Pinching rules in the chiral-splitting description of one-loop string amplitudes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.19641 |