Bootstrapping the Chiral-Gravitational Anomaly

TL;DR

This paper investigates causality and unitarity constraints in theories with gravitational anomalies, establishing bounds on the emergence of high-spin states and implications for axion and gauge theories, including holographic models.

Contribution

It introduces a universal causality scale in anomalous theories, linking it to the emergence of high-spin states and analyzing bounds in various models including axions and holography.

Findings

A universal causality scale $\\Lambda_{\rm caus}$ is identified.

Bounds are derived for axion models relating $\Lambda_{\rm caus}$ to $f_a$ and $M_P$.

Holographic models exhibit a cutoff scale unless specific parameters are met.

Abstract

We analyze causality and unitarity constraints in graviton scattering amplitudes, aiming to establish new bounds on theories with $U(1)$-gravitational anomalies, such as axion models or strongly-coupled gauge theories. For this purpose, we show the necessity of coupling these theories to gravity. We obtain a universal scale $\Lambda_{\rm caus}$ at which states with $J\geq 4$ must appear in the theory. We show that this scale can lie below the quantum gravity scale. For axion models, we get $\Lambda_{\rm caus}\sim\sqrt{M_P f_a}$ where $f_a$ is the axion decay constant. In strongly-coupled gauge theories in the large-$N_c$ limit, the presence of glueballs allows to evade these bounds, provided the number of fermions $N_F\ll N_c$ and the 'tHooft coupling is not large. Nevertheless, for models that have a holographic 5D dual (large 'tHooft coupling), $\Lambda_{\rm caus}$ emerges as a new cutoff scale, unless certain conditions on the parameters of the 5D models are satisfied.