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PreprintCC BY-NC-ND 4.0arXiv

Gauge-invariant thermodynamic description of rotating black strings in 5D minimal supergravity via Kaluza-Klein reduction

  • Yang Yu
  • Peng-Ju Hu
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Abstract

We develop a gauge-invariant formulation of the thermodynamics of rotating black strings in five-dimensional minimal supergravity through Kaluza-Klein reduction. At the two-derivative level, we consistently reduce the bulk action and the Gibbons-Hawking-York boundary term, carefully accounting for the surface contributions induced by the Chern-Simons coupling. The resulting four-dimensional theory is 𝒩=2 supergravity coupled to a single vector multiplet, with prepotential P=1/3√3X13/X0. Employing the Hamiltonian formalism, we establish the quantum statistical relation between the Euclidean on-shell action and the Gibbs free energy. We further compute the leading four-derivative corrections to the thermodynamics of a rotating magnetic black string using the Reall-Santos method. The resulting corrections are in precise agreement with previous results obtained directly for the Kerr-Newman black hole in four-dimensional 𝒩=2 supergravity.

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Cite

BibTeXRIS
BibTeX
@misc{yu2026gaugeinvariant,
  title = {{Gauge-invariant thermodynamic description of rotating black strings in 5D minimal supergravity via Kaluza-Klein reduction}},
  author = {Yang Yu and Peng-Ju Hu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04373},
  eprint = {2611.04373},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04373},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Gauge-invariant thermodynamic description of rotating black strings in 5D minimal supergravity via Kaluza-Klein reduction
AU  - Yang Yu
AU  - Peng-Ju Hu
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04373
UR  - https://arxiv.org/abs/2611.04373
AB  - We develop a gauge-invariant formulation of the thermodynamics of rotating black strings in five-dimensional minimal supergravity through Kaluza-Klein reduction. At the two-derivative level, we consistently reduce the bulk action and the Gibbons-Hawking-York boundary term, carefully accounting for the surface contributions induced by the Chern-Simons coupling. The resulting four-dimensional theory is 𝒩=2 supergravity coupled to a single vector multiplet, with prepotential P=1/3√3X_1^3/X_0. Employing the Hamiltonian formalism, we establish the quantum statistical relation between the Euclidean on-shell action and the Gibbs free energy. We further compute the leading four-derivative corrections to the thermodynamics of a rotating magnetic black string using the Reall-Santos method. The resulting corrections are in precise agreement with previous results obtained directly for the Kerr-Newman black hole in four-dimensional 𝒩=2 supergravity.
ER  -