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arXiv · 2511.06604

The phase of charged Nariai solutions

Victor Ivo·Zimo Sun
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Abstract

In this note, we compute the phase of the one-loop Euclidean path integral around charged Nariai solutions in 4 dimensions, including both metric and gauge field fluctuations. These solutions have a $S^{2} \times S^{2}$ geometry, and a magnetic flux in one of the spheres. For charges smaller than a critical value, the phase matches the result for the uncharged Nariai solution, and for charges bigger than that value, the phase is $i^{3}$. Our analytical calculation in the full 4D geometry matches the result obtained recently within a 2D dilaton gravity reduction. Along the way, we also develop a method of dealing with residue zero modes in the de Donder gauge.

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Victor Ivo, Zimo Sun. 2025-11-10. The phase of charged Nariai solutions. https://arxiv.org/abs/2511.06604

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