Low energy expansion of the four-particle genus-one amplitude in type II superstring theory

Understand

A diagrammatic expansion of coefficients in the low-momentum expansion of the genus-one four-particle amplitude in type II superstring theory is developed.

• This is applied to determine coefficients up to order s^6R^4 (where s is a Mandelstam invariant and R^4 the linearized super-curvature), and partial results are obtained beyond that order.
• This involves integrating powers of the scalar propagator on a toroidal world-sheet, as well as integrating over the modulus of the torus.
• At any given order in s the coefficients of these terms are given by rational numbers multiplying multiple zeta values (or Euler--Zagier sums) that, up to the order studied here, reduce to products of Riemann zeta values.