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<p>We study the Euclidean path integral of higher spin gravity on <i>S</i><sup>4</sup>. Based on a one-loop analysis, we are led to a gluing formula expressing the <i>S</i><sup>4</sup> path integral in terms of an underlying <i>S</i><sup>3</sup> path integral. We view the three-sphere as a boundary hypersurface splitting the four-sphere into two halves. For a higher spin spectrum containing even spins only, the resulting boundary theory living on the <i>S</i><sup>3</sup> cut is the Sp(<i>N</i>) invariant sector of <i>N</i> ∈ <i>ℤ</i><sup>+</sup> anti-commuting, conformally coupled free scalars, with conformal higher spin sources mediating the gluing. This boundary Sp(<i>N</i>) theory was previously shown to compute the Hartle-Hawking wavefunction at <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi mathvariant="script">I</mi> <mo>+</mo> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{I}}^{+} \)</EquationSource> </InlineEquation> in the higher spin dS<sub>4</sub>/CFT<sub>3</sub> correspondence. In contrast to the infinite spatial volume of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi mathvariant="script">I</mi> <mo>+</mo> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{I}}^{+} \)</EquationSource> </InlineEquation>, here the conformal fields populate a finite size <i>S</i><sup>3</sup> hypersurface of <i>S</i><sup>4</sup>. For theories with both bosonic and fermionic higher spin fields, the gluing formula is instead built from an <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 superconformal boundary field theory coupled to <i>U</i> (<i>N</i>) invariant superconformal sources. Under this assumption, the leading contribution to the four-sphere partition function is 2<sup><i>N</i></sup>, and we observe exact cancellations at one-loop.</p>

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dS4 Metamorphosis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月21日

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  • Dionysios Anninos,
  • Chiara Baracco,
  • Vasileios A. Letsios,
  • Beatrix Mühlmann

摘要

We study the Euclidean path integral of higher spin gravity on S4. Based on a one-loop analysis, we are led to a gluing formula expressing the S4 path integral in terms of an underlying S3 path integral. We view the three-sphere as a boundary hypersurface splitting the four-sphere into two halves. For a higher spin spectrum containing even spins only, the resulting boundary theory living on the S3 cut is the Sp(N) invariant sector of N ∈ ℤ+ anti-commuting, conformally coupled free scalars, with conformal higher spin sources mediating the gluing. This boundary Sp(N) theory was previously shown to compute the Hartle-Hawking wavefunction at I + \( {\mathcal{I}}^{+} \) in the higher spin dS4/CFT3 correspondence. In contrast to the infinite spatial volume of I + \( {\mathcal{I}}^{+} \) , here the conformal fields populate a finite size S3 hypersurface of S4. For theories with both bosonic and fermionic higher spin fields, the gluing formula is instead built from an N \( \mathcal{N} \) = 2 superconformal boundary field theory coupled to U (N) invariant superconformal sources. Under this assumption, the leading contribution to the four-sphere partition function is 2N, and we observe exact cancellations at one-loop.