Investigating strongly interacting Quantum Field Theories at finite density via holography

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Quantum Field Theories at finite density of charges conserved in the relativistic domain (such as the baryonic charge in QCD) are not well understood in the regime of strong coupling. Perturbative approach at strong coupling is inadequate and the existing non-perturbative methods (lattice QFT) are constrained by the infamous sign problem. Meanwhile, strong interest in understanding finite density strongly coupled QFTs is prompted by two developments: new purpose-built heavy ion accelerators (FAIR and NICA) scheduled for launch in the next 2-3 years and dedicated precision observations of neutron stars and similar objects. FAIR and NICA will explore the phase diagram of QCD in the region of non-negligeable density with an overall aim of finding the conjectured critical point and investigating nuclear matter in its vicinity. Neutron star observations are aimed at understanding the structure of the cores described by exotic phases of QCD at super-high density. Theoretical understanding of these domains is extremely limited.The proposed line of research will investigate strongly coupled QFTs at finite chemical potential via holography (gauge-string duality). The main objective is to establish properties of the corresponding quantum fluid in this regime and especially in the vicinity of a critical point. This involves building fluid dynamics of chiral fluids to second order and investigating its properties at strong coupling using dual gravity methods and purpose-built QFT models. We hope to come across universal qualitative features in which case the impact on the field will be very significant. At the very least, we shall understand strongly coupled QFTs of a certain type at finite density, where very little is known at the moment.The plan involves, after some preparatory period, building a holographic dual of a known QFT with a conserved charge and investigating its transport properties at first and second order of the derivative expansion. Chiral fluid dynamics appears to have a number of distinct features (some of them are known from optically active media) which can be studies via probes normally used for quark-gluon plasma. At the same time, we shall build a bottom-up holographic model with a critical point to investigate possible signatures of critical behaviour of a strongly coupled chiral medium. A general formalism including the hierarchy f Kubo relations will be constructed.A second, more ambitious stage, will include computing finite coupling corrections to any of the results of stage one. Unfortunately, the existing string theory compactification results allowing one to explore systems with finite density were criticized in the literature as unreliable. Therefore, the first step would be establishing a reliable compactification scheme - this may be rather challenging technically and will be attempted only under favourable conditions.We plan to collaborate with theoretical physicists at University Victoria (Canada) and University of Edinburgh. This project falls within Quantum Field Theory (mostly), String Theory and Mathematical Physics research areas.