Improved Holographic QCD on a Curved Background: an Application of Dynamical System Theory in Holography

The finite-curvature phase diagram of IHQCD, a bottom-up holographic model for large $N_c$ non-supersymmetric YM${}_4$, is investigated. This holographic theory belongs to a class of Einstein-Dilaton theories that exhibit no scaling in the IR. We use advanced techniques from dynamical system theory to address this problem that is harder than other holographic setups. We classify all solutions where the dual theory is defined on a constant curvature manifold, both with positive and negative curvature. For general theories in this class a quantum phase transition occurs at finite curvature. For IHQCD in particular, we find that the phase transition occurs at zero curvature.