Two-loop superstring five-point amplitudes III, construction via the RNS formulation: even spin structures

Abstract

The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genus-two amplitude with four external NS states. The results agree with the parity-even NS components of a construction using chiral splitting and pure spinors given in earlier companion papers arXiv:2006.05270 and arXiv:2008.08687.

93+59 pages, 1 figure; v2: minor touchups; v3: added discussion of overall normalization, to be published in JHEP; v4: corrected misnormalization of parity-odd terms by a factor of 8 in equations (1.11) and (1.12)

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• Integrating three-loop modular graph functions and transcendentality of string amplitudes
• Cyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
• Advanced tools for basis decompositions of genus-one string integrals
• Supermoduli and PCOs at Genus Two
• Singular Spin Structures and Superstrings