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Functional Renormalization - from quantum gravity and dark energy to ultracold atoms and condensed matter

Final Report Summary - FUNREN (Functional Renormalization - from quantum gravity and dark energy to ultracold atoms and condensed matter)

How do new macroscopic laws emerge from microscopic laws or fundamental principles? How can complex macroscopic physics arise from the simplicity of basic microscopic concepts? We have built this bridge from microphysics to macrophysics in three vastly different areas: quantum gravity and cosmology, strong interactions in particle physics and phase transitions in solids and ultracold atoms. The theoretical method has been the same: functional flow equations. They describe how laws depend on a length scale by following the scale-dependence of couplings or functions characterizing these laws. Flow equations act like a theoretical microscope with variable resolution.

For quantum gravity, we have substantially enhanced the evidence that the flow of couplings or functions describing the laws of gravity reaches fixed values as the characteristic distance is shortened further and further. The presence of such an “ultraviolet fixed point” allows combining the principles of general relativity and quantum physics in a quantum field theory for gravity. Our approach to quantum gravity has also found first evidence that the flow towards larger and larger length scales becomes also independent of intrinsic length scales, corresponding to an “infrared fixed point”. The cosmological equations resulting from this crossover between two fixed points lead to solutions with striking properties. Inflation and dynamical dark energy originate from the same scalar field. Our Universe evolves in time from the ultraviolet fixed point in the infinite past to the infrared fix point in the infinite future. The Universe can be eternal, without the need of a big bang singularity. It can be described with different geometrical pictures, for example shrinking and heating instead of expanding and cooling during the epochs of radiation and matter domination.

The microscopic law for strong interactions in elementary particle physics is formulated in terms of quarks and gluons. The observed elementary particles are different, namely protons, neutrons or mesons. On the macroscopic level a complex collective behaviour characterizes hot or dense media of strongly interacting particles (“quark gluon plasma”). Our approach finds the emergence of mesons in a continuous flow from microphysics to macrophysics. Detailed collective properties of hot and dense matter, as the viscosity, have been computed from first principles.

The presence of different phases of macroscopic matter and the properties of phase transitions are key issues for any attempt to compute macroscopic properties from fundamental laws. We have computed phase properties and transitions for rather different microscopic solid state models that describe graphene or multicritical behaviour. Our computation of the phase structure for imbalanced gases of ultracold atoms can be tested experimentally in settings with adjustable interaction strength and density.

The successful work of this ERC advanced grant has helped to establish functional renormalization or functional flow equations as a common method for very different fields in physics. The general acceptance of the method and the community of researchers employing it has increased substantially, and the areas of its application widened.