Discoveries
For superconductors he predicted in 1982 a tricritical point in the phase diagram between type-I and type-II superconductors where the order of the transition changes from second to first. The predictions were confirmed in 2002 by Monte Carlo computer simulations.
The theory is based on a disorder field theory dual to the order field theory of L.D. Landau for phase transitions which Kleinert developed in the books on Gauge Fields in Condensed Matter. In this theory, the statistical properties of fluctuating vortex or defect lines are described as elementary excitations with the help of fields, whose Feynman diagrams are the pictures of the lines.
At the 1978 summer school in Erice he proposed the existence of broken supersymmetry in atomic nuclei, which has since been observed experimentally.
His theory of collective quantum fields and the Hadronization of Quark Theories are prototypes for numerous developments in the theory of condensed matter, nuclear and elementary particle physics.
Together with K. Maki he proposed and clarified in 1981 a possible icosahedral phase of quasicrystals. This structure was discovered three years later in aluminum transition metal alloys by Dan Shechtman, which earned him the Nobel Prize 2011. See historical notes.
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