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Fundamentals and Applications of Holographic Duality

Final Report Summary - HOLOERG (Fundamentals and Applications of Holographic Duality)

Recent ideas originating from string theory postulate a general holographic equivalence between standard quantum mechanical theories of fields and particles and classical and quantum higher-dimensional theories of gravity. This is a fascinating connection with far-reaching implications about the key principles thatshould be applied when formulating the fundamental laws of nature and the practical and mathematical implementation of these laws in systems of interest. Outstanding questions regarding this equivalence are: what are the principles underlying it, what is the range of theoretical systems it applies to and what does it tell us about the properties of physically relevant systems?

Aiming to address these questions in this project we have uncovered qualitatively new examples and applications of the holographic equivalence, novel properties of strongly interacting quantum theories in three dimensions and novel insights into the non-perturbative structure of string/M-theory.

One of the characteristic new applications of holography that we have provided explains how a classical theory of multiple gravitons and spacetimes can be used to describe holographically networks of strongly interacting systems linked to each other by weak inter-site interactions. Such systems, which appear naturally in real-world applications of superconductors and Josephson junctions, are in many cases hard to capture with conventional techniques and the proposed approach offers a radically new look on their properties.

Ultimately, progress in many key topics of theoretical physics (from cosmology and black hole physics to particle physics and condensed matter) relies on the ability to combine the above techniques with the mathematical ability to capture efficiently the exact properties of strongly interacting quantum theories in diverse spacetime dimensions. On this front, we explored new phenomena in quantum field theories in three and four spacetime dimensions and employed recently discovered techniques in classical supergravity theories to uncover previously inaccessible properties of two dimensional quantum field theories that play a central role in the non-perturbative structure of string/M-theory.

A number of national and international collaborations were initiated during the implementation of the project contributing significantly to a positive outcome. However, despite the success of the scientific part, re-integration was impeded by the recent economic crisis that has affected universities and research centers all over the host country, Greece. Because of the freezing of all hirings in the Greek public sector the re-integration of the fellow into the academic society of his home country was not successful and the development of his research carrier was seriously obstructed.