Physical significance of generalized boundary conditions: an Unruh-DeWitt detector viewpoint on $\text{AdS}_2 \times \mathbb{S}^2$

TL;DR

This paper investigates how generalized boundary conditions in AdS2 x S2 affect the response of Unruh-DeWitt detectors, revealing a greater-than-expected freedom in boundary choices with significant physical implications.

Contribution

It constructs two-point functions under generalized boundary conditions and analyzes their impact on detector responses, highlighting the physical significance of boundary condition choices.

Findings

Detector responses vary with boundary parameter b3

Different secondary solutions lead to qualitatively distinct detector behaviors

Boundary condition freedom has notable physical significance

Abstract

On $\text{AdS}_2 \times \mathbb{S}^2$, we construct the two-point correlation functions for the ground and thermal states of a real Klein-Gordon field admitting generalized $(\gamma,v)$-boundary conditions. We follow the prescription recently outlined in [1] for two different choices of secondary solutions. For each of them, we obtain a family of admissible boundary conditions parametrized by $\gamma\in\left[0,\frac{\pi}{2}\right]$. We study how they affect the response of a static Unruh-DeWitt detector. The latter not only perceives variations of $\gamma$, but also distinguishes between the two families of secondary solutions in a qualitatively different, and rather bizarre, fashion. Our results highlight once more the existence of a freedom in choosing boundary conditions at a timelike boundary which is greater than expected and with a notable associated physical significance.