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

TL;DR

This paper establishes a gauge-gravity duality linking massive vector field perturbations in Schwarzschild spacetime with supersymmetric gauge theories, enabling precise analytical computation of quasinormal modes using Seiberg-Witten theory.

Contribution

It introduces a novel mapping of Proca field perturbations to Seiberg-Witten curves, extending the SW/QNM duality to vector fields and providing a new analytical approach for spectral analysis.

Findings

Analytical computation of QNM frequencies matches numerical results.

Extended SW framework to include vector field perturbations.

Resolved spectral properties non-perturbatively using instanton counting.

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 quasi-bound state frequencies to high precision, resolving spectral properties non-perturbatively. Our results align with numerical benchmarks while extending the SW framework beyond scalar fields.