Flavours and Infra-red Instability in Holography

TL;DR

This paper investigates how flavor dynamics and infra-red instabilities manifest in a holographic model of strongly coupled gauge theories, revealing that increasing flavor-to-color ratio suppresses certain instabilities and favors superconducting phases.

Contribution

It demonstrates the impact of flavor-to-color ratio on IR instabilities and phase transitions in a holographic model of strongly coupled gauge theories.

Findings

Superconductor/superfluid instabilities are enhanced with higher N_f/N_c.

Spontaneous translational symmetry breaking is suppressed as N_f/N_c increases.

Results align with large N_c QCD behavior regarding density wave suppression.

Abstract

Within a phenomenological holographic model in $(4+1)$-bulk dimensions, defined by Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld and a Chern-Simons term, we explore the fate of BF-bound violation for a probe scalar field and a fluctuation mode of the corresponding geometry. We assume this simple model to capture the dynamics of a strongly coupled SU$(N_c)$ gauge theory with $N_f$ fundamental matter, which in the limit ${\cal O} \left( N_c \right) \sim {\cal O}\left(N_f\right)$ and with a non-vanishing matter density, is holographically described by an AdS$_2$-geometry in the IR. We demonstrate that, superconductor/superfluid instabilities are facilitated and spontaneous breaking of translational invariance is inhibited with increasing values of $\left(N_f / N_c \right) $. This is similar, in spirit, with known results in large $N_c$ Quantum Chromodynamics with $N_f$ quarks and a non-vanishing density, in which the chiral density wave phase becomes suppressed and superconducting instabilities become favoured as the number of quarks is increased.