  We present the massless six-point one-loop amplitudes in the open and closed
superstring using BRST cohomology arguments from the pure spinor formalism. The
hexagon gauge anomaly is traced back to a class of kinematic factors in pure
spinor superspace which were recently introduced as BRST pseudo-invariants.
This complements previous work where BRST invariance arguments were used to
derive the non-anomalous part of the amplitude. The associated worldsheet
functions are non-singular and demonstrated to yield total derivatives on
moduli space upon gauge variation. These cohomology considerations yield an
efficient organizing principle for closed-string amplitudes that match
expectations from S-duality in the low-energy limit.

High Energy Physics - Theory