Higher-loop amplitudes in the non-minimal pure spinor formalism

Abstract

We analyze the properties of the non-minimal pure spinor formalism. We show that Siegel gauge on massless vertex operators implies the primary field constraint and the level-matching condition in closed string theory by reconstructing the integrated vertex operator representation from the unintegrated ones. The pure spinor integration in the non-minimal formalism needs a regularisation. To this end we introduce a new regulator for the pure spinor integration and an extension of the regulator to allow for the saturation of the fermionic d-zero modes to all orders in perturbation. We conclude with a preliminary analysis of the properties of the four-graviton amplitude to all genus order.

v1: harvmac format. 28 pages. No figures. v2: added references and typos corrected. Expanded discussion of the zero mode counting and the vanishing condition of amplitudes. v3: minor corrections

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• Three-Loop Superfiniteness of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• Ultraviolet properties of Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
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Cited by in corpus (1)

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