Bootstrapping the $a$-anomaly in $4d$ QFTs: Episode II

TL;DR

This paper develops new bounds on the a-anomaly in four-dimensional quantum field theories by analyzing dilaton-coupled scattering amplitudes, providing insights into the structure of gapped QFTs.

Contribution

It introduces a novel method to constrain the a-anomaly using unitarity of scattering amplitudes in coupled dilaton-QFT systems, extending previous bounds.

Findings

Derived new lower bounds on the a-anomaly for various gapped QFTs.

Applied the amplitude-based approach to theories with different numbers of stable scalars.

Enhanced understanding of anomaly constraints in 4d quantum field theories.

Abstract

As recently shown, the a-anomaly of the UV fixed point of 4d quantum field theories, can be constrained by studying scattering amplitudes. The basic idea is to couple the QFT to a dilaton and impose unitarity of the scattering amplitudes of physical particles and probe dilatons. In this work we find new lower bounds on the $a$-anomaly in several gapped QFTs containing different numbers of stable scalar particles.