Physics Group Meeting

The pure spinor formalism is an alternative description of the superstring which is manifestly spacetime supersymmetric and can be covariantly quantized. As a consequence, in recent years many superstring amplitudes which were impractical to calculate using the standard formulations have been computed and the results show a surprising elegance.

In this discussion I will review the superfields in the covariant description of ten-dimensional super Yang--Mills theory and show how their appearance in the vertex operators of the pure spinor string motivated their generalization to a multiparticle setup. Together with the notion of pure spinor superspace and BRST invariance, this framework greatly simplifies the calculations of higher-point amplitudes and leads to compact expressions.

I will focus on the tree-level applications of these ideas culminating in supersymmetric expressions for local BCJ-satisfying kinematic numerators of an arbitrary n-point SYM tree amplitude.

1) Summary in the first three sections of
http://arxiv.org/abs/1510.08843

2) The calculation of the n-point string tree-level amplitude
http://arxiv.org/abs/1106.2645

3) Field-theory applications at tree-level (relation with Berends—Giele method etc)
http://arxiv.org/abs/1510.08846

4) Field-theory applications at one and two loops (in BCJ-satisfying form)
http://arxiv.org/abs/1410.0668

http://arxiv.org/abs/1505.02746

5) The original pure spinor formalism paper is enough for the tree-level discussion
http://arxiv.org/abs/hep-th/0001035

6) For the SYM superfields in 10D

Twistor-Like Transform in Ten-Dimensions
Edward Witten (Princeton U.). May 1985. 39 pp.
Published in Nucl.Phys. B266 (1986) 245