Casimir dynamics: Interactions of Surfaces with codimension >1 due to Quantum Fluctuations

TL;DR

This paper investigates the Casimir force between higher co-dimension defects caused by quantum fluctuations, revealing an attractive force that diverges at a critical distance, leading to vacuum instability and field condensation.

Contribution

It provides a detailed analysis of Casimir interactions for defects with co-dimension greater than one, highlighting the divergence and instability phenomena.

Findings

Casimir force is attractive between higher co-dimension defects

Force diverges at a critical separation distance

Vacuum becomes unstable and condenses below the critical distance

Abstract

We study the Casimir force between defects (branes) of co-dimension larger than 1 due to quantum fluctuations of a scalar field $\phi$ living in the bulk. We show that the Casimir force is attractive and that it diverges as the distance between the branes approaches a critical value $L_c$. Below this critical distance $L_c$ the vacuum state $\phi=0$ of the theory is unstable, due to the birth of a tachyon, and the field condenses.