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

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.

arXiv comment41 pages + appendices, 20 figures. In v2 section 2 improved, minor updates, references added

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