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<p>The standard geometric description of <i>d</i>-dimensional anti-de Sitter (AdS) space is a quadric in ℝ<sup><i>d−</i>1<i>,</i>2</sup> defined by (<i>X</i><sup>0</sup>)<sup>2</sup> − (<i>X</i><sup>1</sup>)<sup>2</sup> − ⋯ − (<i>X</i><sup><i>d−</i>1</sup>)<sup>2</sup> + (<i>X</i><sup><i>d</i></sup>)<sup>2</sup> = <i>ℓ</i><sup>2</sup> = const. In this paper we provide a supersymmetric generalisation of this embedding construction in the <i>d</i> = 5 case. Specifically, a bi-supertwistor realisation is given for the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26332_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>-extended AdS superspace <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26332_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi>AdS</mi> <mrow> <mn>5</mn> <mo>∣</mo> <mn>8</mn> <mi mathvariant="script">N</mi> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\textrm{AdS}}^{5\mid 8\mathcal{N}} \)</EquationSource> </InlineEquation>, with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26332_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. The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a new model for a massive superparticle in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26332_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi>AdS</mi> <mrow> <mn>5</mn> <mo>∣</mo> <mn>8</mn> <mi mathvariant="script">N</mi> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\textrm{AdS}}^{5\mid 8\mathcal{N}} \)</EquationSource> </InlineEquation> which is manifestly invariant under the AdS isometry supergroup SU(2, 2|<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26332_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>) and involves two independent two-derivative terms.</p>

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Embedding formalism for AdS superspaces in five dimensions

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  • 发表日期：

    2025年6月3日

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  • Nowar E. Koning,
  • Sergei M. Kuzenko

摘要

The standard geometric description of d-dimensional anti-de Sitter (AdS) space is a quadric in ℝd−1,2 defined by (X0)2 − (X1)2 − ⋯ − (Xd−1)2 + (Xd)2 = ℓ2 = const. In this paper we provide a supersymmetric generalisation of this embedding construction in the d = 5 case. Specifically, a bi-supertwistor realisation is given for the N \( \mathcal{N} \) -extended AdS superspace AdS 5 ∣ 8 N \( {\textrm{AdS}}^{5\mid 8\mathcal{N}} \) , with N \( \mathcal{N} \) ≥ 1. The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a new model for a massive superparticle in AdS 5 ∣ 8 N \( {\textrm{AdS}}^{5\mid 8\mathcal{N}} \) which is manifestly invariant under the AdS isometry supergroup SU(2, 2| N \( \mathcal{N} \) ) and involves two independent two-derivative terms.