Opacity from Loops in AdS

TL;DR

This paper analyzes how quantum loop effects in Lorentzian AdS influence scalar field propagation, revealing that IR regions become opaque due to exponential damping from loop corrections, with implications for effective field theories in AdS.

Contribution

It provides a detailed computation of the imaginary part of the self-energy in different spectral representations and demonstrates the universal opacity effect caused by loops in AdS, especially in AdS$_5$.

Findings

Loop corrections exponentially dampen IR propagation in AdS.

Different spectral representations of the propagator are shown to be equivalent.

Gravity contributes a universal opacity in AdS$_5$.

Abstract

We investigate how quantum dynamics affects the propagation of a scalar field in Lorentzian AdS. We work in momentum space, in which the propagator admits two spectral representations (denoted "conformal" and "momentum") in addition to a closed-form one, and all have a simple split structure. Focusing on scalar bubbles, we compute the imaginary part of the self-energy $ {\rm Im} \Pi$ in the three representations, which involves the evaluation of seemingly very different objects. We explicitly prove their equivalence in any dimension, and derive some elementary and asymptotic properties of $ {\rm Im} \Pi$. Using a WKB-like approach in the timelike region, we evaluate the propagator dressed with the imaginary part of the self-energy. We find that the dressing from loops exponentially dampens the propagator when one of the endpoints is in the IR region, rendering this region opaque to propagation. This suppression may have implications for field-theoretical model-building in AdS. We argue that in the effective theory (EFT) paradigm, opacity of the IR region induced by higher dimensional operators censors the region of EFT breakdown. This confirms earlier expectations from the literature. Specializing to AdS$_5$, we determine a universal contribution to opacity from gravity.