Semi-holographic quantum field theories and applications

Quantum mechanics tells us that particles do not follow deterministic paths, but we need to sum over all paths to calculate probabilities. In Quantum Field theory (QFTs), the framework to describe most many-body quantum systems in nature, particles can be created and destroyed from the vacuum via actions of quantum fields. We need to sum over histories to calculate probabilities. Remarkably, just as in classical systems, we can capture many-body quantum physics in QFTs using only few relevant couplings at any scale of resolution. The Renormalization Group (RG) flow approach tells us why QFTs indeed work as effective theories in this sense. We understand QFTs well when the couplings, which give local interactions between particles are small. Despite remarkable progress, we do not understand strongly interacting quantum systems generally, where the couplings are large. This is why we do not yet understand nuclear physics from first principles. The main obstacle is the feature called confinement in Quantum Chromodynamics (QCD), the fundamental theory of elementary quarks and gluons of which nuclear matter is made of. Confinement results from strong interactions, and due to it we cannot isolate quarks and gluons from neutrons, protons and pions. The holographic duality, which comes from string theory and has been a major focus of theoretical physics over the past decade, gives a new way to understand special strongly interacting quantum systems of a large number of elementary particles by mapping them to classical theories of gravity in one extra dimension. The Sakai-Sugimoto model obtained via this duality has been partially successful to capture low energy properties of QCD. In this research proposal, an exciting new framework called the semi-holographic framework has been proposed which can integrate together the perturbative methods of QCD which works when the coupling is small at high energy, with the methods of holographic duality which work better at low energy, in order to develop a comprehensive new framework for QCD. The goal is to show first that this framework is indeed effective, in the sense that it can capture all relevant physics via a few parameters, by using numerics and standard analysis, and then to match it with experiments. Furthermore, first steps of a first principle derivation of this framework has been proposed using the RG flow approach.

This project had been proposed to advance a theoretical framework that can unravel fundamental quantum theories involving complex interactions such as those between quarks and gluons which constitute nuclear matter, and those between strongly correlated electrons in high temperature superconductors.A speci?c application had been proposed for describing the phenomenology of Quark-Gluon Plasma, a form of matter which ?lled our Universe when it was a few microseconds old and which has now been recreated in collider experiments at Brookhaven and CERN. The proposal was aimed towards combining different approaches, namely that of Feynman path integrals over elementary particle trajectories and also holographic dual descriptions inspired by string theory in which strong interaction dynamics can be mapped to Einsteins theory of classical gravity in a hyperbolic space of one higher dimension. The need for combining such disparate approaches had been recognised earlier but a consistent method had been lacking.During the course of this project, a lot of progress has been made in postulating, further developing and re?ning such an approach towards quantum many-body dynamics called semi-holography. One key aspect that has been recognised is that one can constrain interactions between different dynamical sectors in which different effective descriptions apply simply via the existence of a conserved energy-momentum tensor for the full system. Furthermore, it has been also been proposed how one can see each sector as a shadow of another in the sense that the parameters of one sector can be deduced from another via some mathematical rules although only one sector typically plays a dominant role at a speci?c energy scale. A toy example has been constructed to illustrate the general principles and a speci?c derivation has been proposed for the theory of quarks and gluons.An upcoming publication will describe a speci?c toy model for the quark-gluon plasma which remarkably captures some aspects of its complex phase transitions and perhaps also collective behaviour phenomenologically. A publication of this project also shows how the semi-holographic approach can lead to a concrete realisation of a novel pairing mechanism in strongly correlated electronic systems that is similar to the mid-infrared scenario proposed earlier by Leggett. Further work is expected to throw new light on possible mechanisms behind high temperature superconductivity.