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<p>We analyze an alternative prescription for computing tree level scattering amplitudes in the pure spinor superstring. Proposed by Berkovits, and inspired by an earlier work by Lee and Siegel, it bypasses the traditional ghost number three measure of the pure spinor ghosts, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\langle {\lambda }^{3}{\theta }^{5}\rangle =1\)</EquationSource> </InlineEquation>, arguably simplifying the calculation. However, direct computations using the free field OPEs of the target superspace CFT fail to reproduce the expected SL(2<i>,</i> ℂ) invariance of tree level correlators. This persistent mismatch, confirmed through independent methods, is not compatible with the gauge invariance of the amplitude. We also discuss possible implications for the B-RNS-GSS formalism of the superstring.</p>

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Tension between string amplitude prescriptions with presumed spacetime supersymmetry

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  • 出版模式：

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  • 发表日期：

    2025年11月19日

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  • Thales Azevedo,
  • Alessandro Georgoudis,
  • Renann Lipinski Jusinskas,
  • Sitender Pratap Kashyap

摘要

We analyze an alternative prescription for computing tree level scattering amplitudes in the pure spinor superstring. Proposed by Berkovits, and inspired by an earlier work by Lee and Siegel, it bypasses the traditional ghost number three measure of the pure spinor ghosts, \(\langle {\lambda }^{3}{\theta }^{5}\rangle =1\) , arguably simplifying the calculation. However, direct computations using the free field OPEs of the target superspace CFT fail to reproduce the expected SL(2, ℂ) invariance of tree level correlators. This persistent mismatch, confirmed through independent methods, is not compatible with the gauge invariance of the amplitude. We also discuss possible implications for the B-RNS-GSS formalism of the superstring.