Pure spinor vertex operators in Siegel gauge and loop amplitude regularization

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Int School Advanced Studies


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 integral 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.



Superstrings and Heterotic Strings, String Field Theory

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Journal of High Energy Physics. Trieste: Int School Advanced Studies, n. 7, p. 30, 2009.