Two-loop computation of the four-particle amplitude in heterotic string theory

Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

“…For example, S-duality of the Type IIB superstring implies that R 4 terms in the low-energy effective action receive no perturbative corections above one-loop [29]. After much effort, this was recently verified in the RNS formalism at two-loops [7][5].…”

“…Furthermore, the complicated nature of the Ramond vertex operator in the RNS formalism [6] makes it difficult to compute amplitudes involving external fermions or Ramond-Ramond bosons. For these reasons, up to now, explicit multiloop computations in the RNS formalism have been limited to four-point two-loop amplitudes involving external Neveu-Schwarz bosons [7][5].…”

“…So if there are no unphysical divergences in the interior of moduli space 7 , this nonrenormalization theorem implies that superstring multiloop amplitudes are perturbatively finite. Previous attempts to prove this non-renormalization theorem using the RNS formalism [32] were unsuccessful because they ignored unphysical poles of the spacetime supersymmetry currents [2] and incorrectly assumed that the integrand of the scattering amplitude was spacetime supersymmetric.…”

“…The second subsection shows how the various terms in the composite b ghost can be expressed in terms of these operators. 7 In light-cone gauge, unphysical divergences in the interior of moduli space could come from singularities between colliding interaction points [12] [31]. In conformal gauge, there are no obvious potential sources for these unphysical divergences in the interior of moduli space since the amplitudes are independent (up to surface terms) of the locations of picture-changing operators.…”

Covariant multiloop superstring amplitudes⁎⁎A more detailed version of these proceedings has been published in Journal for High Energy Physics 0409 (2004) 047.

“…For example, S-duality of the Type IIB superstring implies that R 4 terms in the low-energy effective action receive no perturbative corrections above one-loop [23]. After much effort, this was recently verified in the RNS formalism at two-loops [7,5]. Using the formalism described here, this S-duality conjecture can be easily verified for all loops.…”