$a$-Anomalous Interactions of the Holographic Dilaton

TL;DR

This paper investigates the effective action of the holographic dilaton in the Randall-Sundrum model, linking higher-derivative interactions to the Weyl $a$-anomaly and exploring phenomenological implications.

Contribution

It identifies the nonlinear dilaton action in the RS scenario, relates four-derivative interactions to the $a$-anomaly, and uncovers novel $a$-dependent couplings affecting collider and cosmological physics.

Findings

Four-derivative dilaton self-interaction coefficient matches the Weyl $a$-anomaly.

Discovered new $a$-dependent couplings to light matter fields.

Potential implications for collider phenomenology and cosmology.

Abstract

We explore higher-derivative terms in the low-energy effective action for the dilaton, the Goldstone boson of spontaneously broken scale invariance. Focusing on the simplest holographic realization of spontaneously broken scale invariance, the Randall-Sundrum (RS) scenario, we identify the nonlinear action for the RS dilaton by integrating out Kaluza-Klein graviton modes. The coefficient of a particular four-derivative dilaton self-interaction can be identified with the Weyl $a$-anomaly of the dual conformal field theory, which we use to verify anomaly matching arguments. We also find novel, $a$-dependent couplings of the dilaton to light matter fields. These anomalous interactions can have a significant effect on the collider phenomenology and the cosmology, potentially allowing us to probe the structure of the underlying conformal sector via low-energy physics. The dilaton effective theory also serves as an interesting scalar analog of gravity, and we study solutions to the equation of motion that parallel black holes and cosmologies.