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<p>The Euclidean Gravitational Path Integral has proven remarkably effective in the quantum regime of black hole physics. In this work, we examine the applicability of the Kontsevich-Segal-Witten (KSW) criterion for admissible complex metrics in the context of the Euclidean Gravitational Path Integral. We find that, for the super-conformal index of 𝒩 = 4 SYM with unequal angular momenta, the black hole saddle points violate the KSW criterion precisely where the statistical description of the index breaks down. The corresponding critical point coincides with a phase transition into two-component “grey galaxy” configurations.</p>

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Allowable complex Black Holes in the Euclidean Gravitational Path Integral

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  • 发表日期：

    2026年6月3日

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  • Vineeth Krishna,
  • Finn Larsen

摘要

The Euclidean Gravitational Path Integral has proven remarkably effective in the quantum regime of black hole physics. In this work, we examine the applicability of the Kontsevich-Segal-Witten (KSW) criterion for admissible complex metrics in the context of the Euclidean Gravitational Path Integral. We find that, for the super-conformal index of 𝒩 = 4 SYM with unequal angular momenta, the black hole saddle points violate the KSW criterion precisely where the statistical description of the index breaks down. The corresponding critical point coincides with a phase transition into two-component “grey galaxy” configurations.