Bootstrapping the chiral-gravitational anomaly

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 Λ_caus at which states with J ≥ 4 must appear in the theory. We show that this scale can lie below the quantum gravity scale. For axion models, we get Λ_caus ∼ \(\sqrt{{M}_{P}{f}_{a}}\) 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 ≪ N_c and the ’tHooft coupling is not large. Nevertheless, for models that have a holographic 5D dual (large ’tHooft coupling), Λ_caus emerges as a new cutoff scale, unless certain conditions on the parameters of the 5D models are satisfied.