Quantum supergravity on curved spacetimes
Final Report Abstract
Quantum field theory has been spectacularly successful in describing the physics of elementary particles at a fundamental level so far. Indeed, the celebrated Standard Model of Particle Physics and the predictions of this theory have been experimentally verified with an outstanding precision which is ever increasing in ongoing experiments. On the other hand, Einstein’s theory of general relativity is undoubtedly a very successful and far-reaching fundamental theory of gravity which has not only allowed us to understand the dynamics of our solar system in great detail and with a great accuracy but also enabled us to obtain a good understanding of the history and development of our whole universe, just with the power of our minds and the help of sophisticated solar system-bound telescopes. Notwithstanding the curved nature of our universe as a spacetime, elementary particle physics is mostly dealt with in the framework of quantum field theory in the flat Minkowski spacetime. This is of course well motivated if one is considering phenomena which happen on spatial and temporal scales which are much smaller than the scales related to the spacetime curvature, i.e. in regimes where gravity is “weak”. But of course there are situations where gravity is “strong”, e.g. in the vicinity of black holes or in the early universe. In these contexts, quantum field theory on curved spacetimes is presumably better suited to describe phenomena in elementary particle physics than quantum field theory in flat spacetime. Supergravity theories are the outcome of promoting rigid supersymmetry in Minkowski spacetime to a local gauge symmetry on curved spacetimes. All supergravity models contain a number of gravitino fields, where the gravitino field is the so-called “superpartner” of the gravitational metric field. The gravitino is a possible candidate for being the constituent of Dark Matter, a yet opaque matter component in our universe which dominates the well-known baryonic matter and interacts considerably only via the gravitational force. In this project I have investigated various aspects of quantum field theory on curved spacetime which are relevant for a full construction of quantum supergravity on general curved backgrounds and phenomenological applications of such a construction. First I have developed a more fundamental understanding of the quantum theory of cosmological perturbations. I first demonstrated how linear perturbations of the Einstein-Klein-Gordon-system can be quantized in a gauge-invariant way on arbitrary curved spacetimes. On cosmological backgrounds, I have compared this with the standard approach to quantizing cosmological perturbations and have found and interpreted essential discrepancies. In a joint work with Alexander Schenkel and Florian Hanisch, we have demonstrated how to treat field theories on supermanifolds in the language of locally covariant quantum field theory. In particular, using techniques from enriched category theory, we have shown how replacing the usual morphism sets by supersets of morphisms which contain supersymmetry transformations as their higher superpoints leads to a framework where only quantized superfields themselves, rather than their individual components, are covariant objects. With the group of my host Nicola Pinamonti, I have developed a renormalization scheme on general curved spacetimes, which manifestly preserves any spacetime isometries present, and is, in contrast to more traditional approaches, directly applicable to Lorentzian spacetimes, manifestly generally covariant and suitable for explicit computations, e.g. in general cosmological spacetimes. Moreover we have developed a conceptual understanding of the thermal mass idea and generalisations thereof in curved spacetimes, in particular we have proven that correlation functions for massless fields in thermal states on Minkowski spacetime are infrared finite at all orders in perturbation theory.
Publications
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Quantization of the linearised Einstein-Klein-Gordon system on arbitrary backgrounds and the special case of perturbations in Inflation, Class. Quantum Grav. 31 (2014) 215004
T.-P. Hack
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An analytic regularisation scheme on curved spacetimes with ´ ´ applications to cosmological spacetimes
A. Géré, T.-P. Hack, N. Pinamonti
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Supergeometry in locally covariant quantum field theory
T.-P. Hack, F. Hanisch, A. Schenkel
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The generalised principle of perturbative agreement and the thermal mass
N. Drago, T.-P. Hack, N. Pinamonti
