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arXiv · 2605.28737

Complex BPS Black Holes in AdS$_3\times S^3$

Finn Larsen·Kartik Sharma
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Abstract

The correct gravitational representation of the supersymmetric index is a smooth complex solution, rather than the na\"{\i}ve Euclidean continuation of the Lorentizan BPS black hole. We construct such saddles for black holes with \(\mathrm{AdS}_3\times S^3\) boundary conditions in the STU model. We arrive at the same finite-temperature BTZ \(\times S^3\) geometries in two independent ways: from two-center four-dimensional BPS solutions with complex dipole charges, and from six-dimensional black strings after imposing the BPS relation among conserved charges. We analyze the resulting smoothness and periodicity conditions and show that they are precisely those required for globally well-defined supersymmetry and for the thermodynamic potentials of the supersymmetric index.

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Finn Larsen, Kartik Sharma. 2026-05-27. Complex BPS Black Holes in AdS$_3\times S^3$. https://arxiv.org/abs/2605.28737

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