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

TL;DR

This paper investigates the phase diagram of Improved Holographic QCD on curved backgrounds using dynamical system theory, revealing a zero-curvature phase transition specific to the model.

Contribution

It applies advanced dynamical system techniques to classify solutions of IHQCD on curved manifolds, identifying the nature of phase transitions in this holographic model.

Findings

Phase transition occurs at zero curvature in IHQCD.

Classified all solutions on constant curvature manifolds.

Demonstrated the complexity of holographic models with no IR scaling.

Abstract

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.