We consider Weyl’s conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a [Formula: see text] term in moving from the Jordan frame to the Einstein frame. A massless Nambu–Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent to the corresponding theory in the Einstein frame via the BRST formalism.

中文翻译：

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外尔共形引力的希格斯势

我们考虑外尔的保形引力耦合到外尔几何中的复杂物质场。结果表明，希格斯势自然产生于 [公式：见正文] 从 Jordan 框架移动到 Einstein 框架的项。源于外尔规范不变性的自发对称性破坏的无质量南部-戈德斯通玻色子被吸收到外尔规范场中，从而使规范场变得有质量。我们提出了一个模型，其中引力相互作用产生了一个希格斯势，其形式是一个完美的正方形。最后，我们通过 BRST 形式证明了 Jordan 框架中的理论与 Einstein 框架中的相应理论是规范等价的。