Bootstrapping the $a$-anomaly in $4d$ QFTs

TL;DR

This paper develops a numerical bootstrap approach to establish lower bounds on the $a$-anomaly in 4d gapped QFTs derived from UV CFTs, using assumptions like unitarity, crossing symmetry, and analyticity.

Contribution

It introduces a method to bound the $a$-anomaly in 4d QFTs based on scattering amplitudes and non-perturbative parameters, expanding bootstrap techniques.

Findings

Derived numerical lower bounds on the $a$-anomaly.

Demonstrated the impact of scattering amplitude parameters.

Provided constraints consistent with known theories.

Abstract

We study gapped 4d quantum field theories (QFTs) obtained from a relevant deformation of a UV conformal field theory (CFT). For simplicity, we assume the existence of a $\mathbb{Z}_2$ symmetry and a single $\mathbb{Z}_2$-odd stable particle and no $\mathbb{Z}_2$-even particles at low energies. Using unitarity, crossing and the assumption of maximal analyticity we compute numerically a lower bound on the value of the $a$-anomaly of the UV CFT as a function of various non-perturbative parameters describing the two-to-two scattering amplitude of the particle.