Carrollian $\mathbb{R}^\times$-bundles II: Sigma Models on Event Horizons

Andrew James Bruce

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arXiv · 2507.00544

Carrollian $\mathbb{R}^\times$-bundles II: Sigma Models on Event Horizons

Andrew James Bruce

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Abstract

Carrollian field theories are usually understood as limits of relativistic theories. In this note, we use Carrollian $\mathbb{R}^\times$-bundles equipped with a principal connection to construct Carrollian sigma models intrinsically. The resulting theories are neither ``electric'' nor ``magnetic'' in the usual sense. As a physically suggestive example, we derive a Carrollian wave equation governing the dynamics of a scalar field on the event horizon of a Schwarzschild black hole.

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Andrew James Bruce. 2025-07-01. Carrollian $\mathbb{R}^\times$-bundles II: Sigma Models on Event Horizons. https://arxiv.org/abs/2507.00544

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