Cohomology foundations of one-loop amplitudes in pure spinor superspace

Understand

We describe a pure spinor BRST cohomology framework to compactly represent ten-dimensional one-loop amplitudes involving any number of massless open- and closed-string states.

• The method of previous work to construct scalar and vectorial BRST invariants in pure spinor superspace signals the appearance of the hexagon gauge anomaly when applied to tensors.
• We study the systematics of the underlying BRST anomaly by defining the notion of pseudo-cohomology.
• This leads to a rich network of pseudo-invariant superfields of arbitrary tensor rank whose behavior under traces and contractions with external momenta is determined from cohomology manipulations.