Cohomology foundations of one-loop amplitudes in pure spinor superspace

Abstract

We describe a pure spinor BRST cohomology framework to compactly represent ten-dimensional one-loop amplitudes involving any number of massless open- and closed-string states. The method of previous work to construct scalar and vectorial BRST invariants in pure spinor superspace signals the appearance of the hexagon gauge anomaly when applied to tensors. We study the systematics of the underlying BRST anomaly by defining the notion of pseudo-cohomology. This leads to a rich network of pseudo-invariant superfields of arbitrary tensor rank whose behavior under traces and contractions with external momenta is determined from cohomology manipulations. Separate papers will illustrate the virtue of the superfields in this work to represent one-loop amplitudes of the superstring and of ten-dimensional super-Yang--Mills theory.

arXiv comment94 pages, harvmac TeX

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Cited by in corpus (12)

• Elliptic multiple zeta values and one-loop superstring amplitudes
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Gauge and Gravity Amplitude Relations
• One-loop Correlators and BCJ Numerators from Forward Limits
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
• One-loop diagrams with quadratic propagators from the worldsheet
• Infrared behaviour of the one-loop scattering equations and supergravity integrands
• Scattering equations, supergravity integrands, and pure spinors
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Towards the quantization of the non-relativistic D2-brane in the Pure Spinor Formalism