Two-loop superstring five-point amplitudes. Part I. Construction via chiral splitting and pure spinors

• Published in: The journal of high energy physics 2020-08, Vol.2020 (8), p.1-80, Article 135
• Main Authors: D’Hoker, Eric, Mafra, Carlos R., Pioline, Boris, Schlotterer, Oliver
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High Energy Physics - Theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; String Theory; Supergravity Models; Superstrings and Heterotic Strings
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP08(2020)135

A bstract The full two-loop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two moduli space of compact Riemann surfaces and integrals of Green functions and Abelian differentials on the surface. The construction combines elements from the BRST cohomology of the pure spinor formulation and from chiral splitting with the help of loop momenta and homology invariance. The α ′ → 0 limit of the resulting superstring amplitude is shown to be in perfect agreement with the previously known amplitude computed in Type II supergravity. Investigations of the α ′ expansion of the Type II amplitude and comparisons with predictions from S-duality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genus-two amplitude with five external NS states is relegated to a second companion paper.