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arXiv · 0903.3443

Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization

Yuri Aisaka·Nathan Berkovits
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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 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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Yuri Aisaka, Nathan Berkovits. 2009-05-27. Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization. https://doi.org/10.1088/1126-6708/2009/07/062

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