Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization

Details Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization

2009-03-20

arxiv.org/abs/0903.3443v2

JHEP 0907:062,2009

Physics

High Energy Physics

High Energy Physics - Theory

30 pages latex, added references and comments to Grassi-Vanhove paper

Scientific paper

10.1088/1126-6708/2009/07/062

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 b_0 V=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 b_0 V* and Siegel gauge integrated vertex operators as \int dz b_{-1} b_0 V*. 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.

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