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

Understand

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 $\alpha'$.
• 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 $\alpha'$-order carries an additional factor of $-3/5$.