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<p>We construct and study the supersymmetry properties of the weighted projective spaces ๐•Žโ„‚โ„™<sup>2</sup> and ๐•Žโ„‚โ„™<sup>3</sup>. These are topologically โ„‚โ„™<sup><i>n</i></sup> with <i>n</i> + 1 orbifold singularities and as such are higher dimensional analogues of the โ€œspindleโ€ or ๐•Žโ„‚โ„™<sup>1</sup>. We use these to construct interesting supersymmetric orbifolds of canonical near horizon geometries of relevance to the AdS/CFT correspondence. Interestingly, for certain tunings of their integer weights, and unlike the spindle, ๐•Žโ„‚โ„™<sup>2</sup> and ๐•Žโ„‚โ„™<sup>3</sup> are compatible with supersymmetry beyond the realm of gauged supergravity. This allows one to construct interesting supersymmetric solutions in type II supergravity such as AdS<sub>5</sub> ร— ๐•Žโ„‚โ„™<sup>2</sup> ร— S<sup>1</sup> and AdS<sub>4</sub> ร— ๐•Žโ„‚โ„™<sup>3</sup> via duality, in which ๐•Žโ„‚โ„™<sup><i>n</i></sup> appears without a connection fibred over it. We also leverage our results to construct a supersymmetric AdS<sub>3</sub> solution containing a topological ๐•‹<sup>(1,1)</sup> space with 4 orbifold singularities.</p>

้”™่ฏฏ๏ผšๆœ็ดขๅ†…ๅฎนไธ่ƒฝไธบ็ฉบ๏ผŒ่ฏท่พ“ๅ…ฅ่‹ฑๆ–‡ๅ…ณ้”ฎ่ฏ
้”™่ฏฏ๏ผšๅ…ณ้”ฎ่ฏ่ถ…ๅ‡บๅญ—ๆ•ฐ้™ๅˆถ๏ผŒ่ฏท็ฒพ็ฎ€
้ซ˜็บงๆฃ€็ดข

Supersymmetric ๐•Žโ„‚โ„™n, AdS near horizons and orbifolds

  • ๆœŸๅˆŠ่ฎบๆ–‡

  • ๅ‡บ็‰ˆๆจกๅผ๏ผš

    ๅผ€ๆ”พ่Žทๅ–

  • ๅ‘่กจๆ—ฅๆœŸ๏ผš

    2026ๅนด5ๆœˆ19ๆ—ฅ

ๆŸฅ็œ‹ๅ…จๆ–‡
  • Andrea Conti,
  • Niall T. Macpherson

ๆ‘˜่ฆ

We construct and study the supersymmetry properties of the weighted projective spaces ๐•Žโ„‚โ„™2 and ๐•Žโ„‚โ„™3. These are topologically โ„‚โ„™n with n + 1 orbifold singularities and as such are higher dimensional analogues of the โ€œspindleโ€ or ๐•Žโ„‚โ„™1. We use these to construct interesting supersymmetric orbifolds of canonical near horizon geometries of relevance to the AdS/CFT correspondence. Interestingly, for certain tunings of their integer weights, and unlike the spindle, ๐•Žโ„‚โ„™2 and ๐•Žโ„‚โ„™3 are compatible with supersymmetry beyond the realm of gauged supergravity. This allows one to construct interesting supersymmetric solutions in type II supergravity such as AdS5 ร— ๐•Žโ„‚โ„™2 ร— S1 and AdS4 ร— ๐•Žโ„‚โ„™3 via duality, in which ๐•Žโ„‚โ„™n appears without a connection fibred over it. We also leverage our results to construct a supersymmetric AdS3 solution containing a topological ๐•‹(1,1) space with 4 orbifold singularities.