On the stability of holographic confinement with magnetic fluxes

Abstract: We analyze the stability properties of a simple holographic model for a confining field theory. The gravity dual consists of an Abelian gauge field, with non-trivial magnetic flux, coupled to six-dimensional gravity with a negative cosmological constant. We construct a one-parameter family of regular solitonic solutions, where the gauge field carries flux along a compact circle that smoothly shrinks. The free energy of these solitonic backgrounds is compared to that of domain-wall solutions. This reveals a zero-temperature first-order phase transition in the dual field theory, separating confining and conformal phases. We compute the spectrum of bound states by analysing field fluctuations in the gravity background, after dimensional reduction on the circle. A tachyonic instability emerges near a turning point in the free energy. The phase transition prevents the realisation of this instability. Near the phase transition and beyond, in metastable and unstable regions, we find evidence that the lightest scalar may be interpreted as an approximate dilaton.