The two-loop superstring five-point amplitude and S-duality

Abstract

The low-energy limit of the massless two-loop five-point amplitudes for both type IIA and type IIB superstrings is computed with the pure spinor formalism and its overall coefficient determined from first principles. For the type IIB theory, the five-graviton amplitude is found to be proportional to its tree-level counterpart at the corresponding order in ${\alpha }^{\prime }$. Their ratio ties in with expectations based on S-duality since it matches the same modular function $E_{5/2}$ which relates the two-loop and tree-level four-graviton amplitudes. For R-symmetry violating states, the ratio between tree-level and two-loop amplitudes at the same ${\alpha }^{\prime }$-order carries an additional factor of $-3/5$. Its S-duality origin can be traced back to a modular form derived from $E_{5/2}$.

42 pages, harvmac tex

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• Tree-level amplitudes from the pure spinor superstring
• Double-Copy Structure of One-Loop Open-String Amplitudes
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
• Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
• Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes
• Two-loop superstring five-point amplitudes III, construction via the RNS formulation: even spin structures
• Fermionic one-loop amplitudes of the RNS superstring
• Cyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
• Pure spinor formulation of the superstring and its applications
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Transcendentality violation in type IIB string amplitudes