Holography for Sp(2$N_c$) Gauge Dynamics: from Composite Higgs to Technicolour

TL;DR

This paper investigates Sp(2$N_c$) gauge theories with two Dirac fermions, exploring their potential to realize composite Higgs and technicolour models through gauge/gravity duality, and analyzing the spectrum and symmetry breaking patterns.

Contribution

It introduces a gauge/gravity duality model that incorporates $N_c$-dependent fermion anomalous dimensions to distinguish gauge groups and studies the spectrum and symmetry breaking in Sp(2$N_c$) theories.

Findings

Identification of the light pseudo-Goldstone bosons as Higgs candidates.

Demonstration of $N_c$-dependent fermion mass spectra.

Emergence of three Goldstone bosons with four-fermion interactions.

Abstract

We study Sp(2$N_c$) gauge dynamics with two Dirac fermion flavours in the fundamental representation. These strongly coupled systems underlie some composite Higgs models with a global symmetry breaking pattern SU(4)$\rightarrow$Sp(4), leading to a light quartet of pseudo-Goldstone bosons that can play the role of the Higgs. Including four-fermion interactions can rotate the vacuum to a technicolour breaking pattern. Using gauge/gravity duality, we study the underlying gauge dynamics. Our model incorporates the $N_c$-specific running of the fermion anomalous dimension and can thus distinguish between specific gauge groups. We determine the bound-state spectrum of the UV SU(4)$\rightarrow$Sp(4) symmetry breaking model, also including fermion masses and mass splitting, and display the $N_c$ dependence. The inclusion of a four-fermion interaction shows the emergence of three Goldstone bosons on the path to technicolour dynamics.