Monodromy relations from twisted homology. (English) Zbl 1431.83163
Summary: We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations involving loop integrands of open-string theories for any number of external particles and, for the first time, to arbitrary genus. In the non-planar sector, these relations contain seemingly unphysical contributions, which we argue clarify mismatches in previous literature. The text is mostly self-contained and presents a concise introduction to twisted homologies. As a result of this powerful formulation, we can propose estimates on the number of independent loop integrands based on Euler characteristics of the relevant configuration spaces, leading to a higher-genus generalization of the famous \((n-3)!\) result at genus zero.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
| 81V73 | Bosonic systems in quantum theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 53Z05 | Applications of differential geometry to physics |
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