Multi-Representation Dynamics of SU(4) Composite Higgs Models: Chiral Limit and Spectral Reconstructions

TL;DR

This paper investigates the non-perturbative spectrum of an SU(4) gauge theory with multiple fermion representations, advancing understanding of composite Higgs models with richer dynamics.

Contribution

It develops methodologies for spectrum computation and chiral extrapolation in multi-representation theories, bridging perturbative and non-perturbative analyses.

Findings

Spectral properties of SU(4) with multiple fermion representations analyzed.

Methodologies for chiral limit extrapolation established.

Non-perturbative spectral reconstructions demonstrated.

Abstract

We present a lattice study of the $SU(4)$ gauge theory with two Dirac fermions in the fundamental and two in the two-index antisymmetric representation, a model close to a theory of partial compositeness. Focus of this work are the methodologies behind the computation of the spectrum and the extrapolation of the chiral point for a theory with matter in multiple representations. While being still technical, this study provides important steps towards a non-perturbative understanding of the spectrum of theories of partial compositeness, which present a richer dynamics compared to single-representation theories. The multi-representation features are studied first in perturbation theory, and then non-perturbatively by adopting a dual outlook on lattice data through a joint analysis of time-momentum correlation functions and smeared spectral densities.