Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization

Abstract

Since the b ghost in the pure spinor formalism is a composite operator depending on non-minimal variables, it is not trivial to impose the Siegel gauge condition b0V = 0 on BRST-invariant vertex operators. Using the antifield vertex operator V ∗ of ghost-number +2, we show that Siegel gauge unintegrated vertex operators can be constructed as b0V ∗ and Siegel gauge integrated vertex operators as ∫ dz b−1b0V . These Siegel gauge vertex operators depend on the non-minimal variables, so scattering amplitudes involving these operators need to be regularized using the prescription developed previously with Nekrasov. As an example of this regularization prescription, we compute the four-point one-loop amplitude with four Siegel gauge integrated vertex operators. This is the first one-loop computation in the pure spinor formalism that does not require unintegrated vertex operators. yuri@ift.unesp.br nberkovi@ift.unesp.br

Cite this paper

@inproceedings{Aisaka2009PureSV, title={Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization}, author={Yuri Aisaka and Nathan Berkovits}, year={2009} }