Advanced tools for basis decompositions of genus-one string integrals
arXiv:2403.18078 · doi:10.1007/JHEP05(2024)255
Abstract
In string theories, one-loop scattering amplitudes are characterized by integrals over genus-one surfaces using the Kronecker-Eisenstein series. A recent methodology proposed a genus-one basis formed from products of these series of chain topologies. A prior work further deconstructed cyclic products of the Kronecker-Eisenstein series on this basis. Building on it, our study further employs advanced and comprehensive combinatorial techniques to decompose more general genus-one integrands including a product of an arbitrary number of cyclic products of Kronecker-Eisenstein series, supplemented by {\tt Mathematica} codes. Our insights enhance the understanding of multiparticle amplitudes across various string theories and illuminate loop-level parallels with string tree-level amplitudes.
44+9 pages, 9 figures
References in corpus (11)
- Minimal Basis for Gauge Theory Amplitudes
- Combinatorics and Topology of Kawai-Lewellen-Tye Relations
- Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
- Amplitude relations in heterotic string theory and Einstein-Yang-Mills
- Duals of Feynman Integrals, 2: Generalized Unitarity
- Current Algebra on the Torus
- All-order differential equations for one-loop closed-string integrals and modular graph forms
- Labelled tree graphs, Feynman diagrams and disk integrals
- Generating series of all modular graph forms from iterated Eisenstein integrals
- Monodromy relations from twisted homology
- Basis decompositions of genus-one string integrals