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Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory

Xian-Hui Ge1,*, Masataka Matsumoto2,3,†, and Kilar Zhang1,4,5,‡

  • 1Department of Physics and Institute for Quantum Science and Technology, Shanghai University, 99 Shangda Road, Shanghai 200444, China
  • 2Department of Physics, Chuo University, Tokyo 112-8551, Japan
  • 3Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • 4Shanghai Key Lab for Astrophysics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, China
  • 5Shanghai Key Laboratory of High Temperature Superconductors, Shanghai 200444, China

  • *Contact author: gexh@shu.edu.cn
  • †Contact author: mmatsumoto173@g.chuo-u.ac.jp
  • ‡Contact author: kilar@shu.edu.cn
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Phys. Rev. D 112, 046024 – Published 28 August, 2025

DOI: https://doi.org/10.1103/3dwl-gg8g

Abstract

We unify the dynamics of massive vector (Proca) fields in Schwarzschild spacetime with supersymmetric gauge theories through the Seiberg-Witten/quasinormal mode (SW/QNM) duality. By mapping Proca perturbations—specifically monopole and odd-parity modes governed by confluent Heun equations—to the quantum Seiberg-Witten curve, we establish a gauge-gravity correspondence. Leveraging instanton counting, we analytically compute QNM and quasibound state frequencies to high precision, resolving spectral properties nonperturbatively. Our results align with numerical benchmarks while extending the SW framework beyond scalar fields.

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Phys. Rev. D 112, 046024– Published 28 August, 2025
  • Received 6 July 2025
  • Accepted 9 August 2025
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