<p>By extending the six-dimensional hybrid formalism for the superstring to include <i>d</i> = 6 <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27097_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 superspace variables along with unconstrained bosonic ghost fields, we construct a manifestly spacetime supersymmetric vertex operator <i>U</i>. We demonstrate that the BRST invariance of <i>U</i> implies the <i>d</i> = 6 <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27097_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 SYM equations of motion in superspace. Furthermore, we show that spacetime supersymmetric scattering amplitudes can be computed in a manner analogous to that of the non-minimal pure spinor formalism.</p>

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Vertex operators for the superstring with manifest d = 6 \( \mathcal{N} \) = 1 supersymmetry

  • Cassiano A. Daniel

摘要

By extending the six-dimensional hybrid formalism for the superstring to include d = 6 N \( \mathcal{N} \) = 1 superspace variables along with unconstrained bosonic ghost fields, we construct a manifestly spacetime supersymmetric vertex operator U. We demonstrate that the BRST invariance of U implies the d = 6 N \( \mathcal{N} \) = 1 SYM equations of motion in superspace. Furthermore, we show that spacetime supersymmetric scattering amplitudes can be computed in a manner analogous to that of the non-minimal pure spinor formalism.