A Holographic study of high-density matter and astrophysical applications

Abstract

In this thesis we study a variety of physical phenomena using the Gauge/Gravity duality to model the symmetries that mimic QCD in the field side at the strong regime, by studying weakly coupled fields in a fixed AdS space-time. We compute the gauge dependent quark condensate in the colour superconducting phase. We construct a holographic dual of the condensate by arguing that near the chiral restoration transition, the strongly coupled gluons are gapped so that the colour quantum numbers of the quarks can be thought of below that gap as global indices. An AdS/superconductor model is then used to analyze the fermionic gap formation. We investigate the role of four fermion interactions to include the gapped QCD interactions. It turns out to be easiest to relate the interaction of the holographic superconductor to the strength of the gapped gluons. The result is a holographic description of the QCD colour superconducting phase diagram. We take a first look at how quark mass enters and causes a transition between the colour flavour locked phase and the 2SC phase. Next we adjust the D3/D7 model to include a running anomalous dimension for the chiral quark condensate. This introduces a mechanism for chiral symmetry breaking, yet the model still has a deconfined massive phase at intermediate densities. We show that these systems, dependent on the running profile in the IR, generate stiffer equations of state than the base D3/D7 model, and a non-monotonic behaviour in the speed of sound. We show that this model support hybrid compact stars with quark cores. Finally we present a model with a first order chiral restoration phase transition with chemical potential, µ, due to a discontinuity in the dual description as the quarks are integrated out below their constituent mass. The model predicts a deconfined, massive quark phase at intermediate densities (350MeV< µ < 550MeV). This phase, has a very stiff equation of state and a speed of sound close to the speed of light. We also include a holographic description of a colour superconducting condensate in the chirally restored vacuum which provides a first order transition from the deconfined massive quark phase at very high density (µ > 550MeV). We solve the TOV equations and find stable hybrid stars with quark cores and with values of the tidal deformabilities that provide an excellent fit to the gravitational wave data GW170817 of LIGO and Virgo.

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