Flavours and Infra-red Instability in Holography

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 $\mathcal{O}\left(N_c\right)\sim \mathcal{O}\left(N_f\right)$ 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.

24 pages, 2 figures

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