Singular interactions supported by embedded curves

TL;DR

This paper investigates singular interactions along embedded curves on Riemannian manifolds using the heat kernel method, establishing a well-defined, finite, and positive ground state with renormalization group invariance.

Contribution

It introduces a direct physical approach to singular interactions supported by embedded curves, demonstrating renormalization and stability properties.

Findings

Renormalized problem is well defined.

Ground state is finite and positive.

Model exhibits renormalization group invariance.

Abstract

In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the ground state is finite and the corresponding wavefunction is positive. The renormalization group invariance of the model is also discussed.