Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 12, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP12(2022)162
Keywords
Superstrings and Heterotic Strings; Differential and Algebraic Geometry
Categories
Funding
- EPSRC [EP/R014604/1]
- Munich Institute for Astro-, Particle and BioPhysics (MIAPbP) - Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy [EXC-2094 - 390783311]
- Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+ [39083149]
- IMPRS for Mathematical and Physical Aspects of Gravitation, Cosmology and Quantum Field Theory
- Engineering and Physical Sciences Research Council [EP/W52251X/1]
- European Research Council [ERC-STG-804286 UNISCAMP]
- Knut and AliceWallenberg Foundation [KAW2018.0162]
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In this paper, we provide validation for Brown's conjecture that equivariant iterated Eisenstein integrals contain modular graph forms beyond depth one. Through various examples and detailed explanations, we reveal the systematic nature of the dictionary and make certain elements of Brown's construction explicit to all orders.
The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called equivariant iterated Eisenstein integrals. In this work, we provide the first validations beyond depth one of Brown's conjecture that equivariant iterated Eisenstein integrals contain modular graph forms. Apart from a variety of examples at depth two and three, we spell out the systematics of the dictionary and make certain elements of Brown's construction fully explicit to all orders.
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