Friday, February 03, 2006

Berkovits string field theory

The last time we discussed the topic of the pure spinor formalism on this blog was here.

Nathan Berkovits is visiting Harvard and he also delivered an interesting seminar. He described the pure spinor formalism in two different editions:
  • the minimal one, with X,theta,lambda being the only fields
  • a non-minimal one with some auxilliary fields
The OPEs and the formulae for the scattering amplitudes involving composite b-antighosts are constructed in both of these pictures, although the proof of their equivalence is only known for a subset of the scattering amplitudes with small enough genus.

It is generally hard to extend Witten's cubic Chern-Simons-like string field theory to the case of RNS superstrings because the RNS formalism requires the picture changing operators that look awkward in the string field language. However, with Berkovits' pure spinor degrees of freedom, superstring field theory can again be written in a simple cubic form because Berkovits' picture is, in some moral sense, more analogous to the bosonic string. Nathan has discussed some subtle variations of the string field theory that differ by insertions at the interaction point. These subtleties are somewhat analogous to the case of twistor string field theory.

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