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 [29] and [33].
Highlights
The study of perturbative scattering amplitudes in string theory dates back to the founding of the subject and continues to provide deep insights into the dynamics of string theory today
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
Summary
The study of perturbative scattering amplitudes in string theory dates back to the founding of the subject and continues to provide deep insights into the dynamics of string theory today. We present a variety of new simplified spin structure sums of multiple products of Szegö kernels and streamline the manipulations of the Beltrami differentials in the moduli-space integrand These new techniques will be, no doubt, crucial for subsequent investigations of multiparticle and higher-genus amplitudes. Our results may be of use in relating the correlators of the ambi-twistor string [42, 43] to those of the conventional superstring [44, 45] This relation was already used in the proposal of [46] for the genus-three four-point amplitude as an uplift of the low-energy limit of the amplitude derived in [28] to higher orders in α. The final expression for the amplitude is, remarkably simple and we shall begin by a summary in the sequel of this introduction
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