Olaf Lechtenfeld is a German mathematical physicist, academic and researcher. He is a full professor at the Institute of Theoretical Physics at Leibniz University, where he founded the Riemann Center for Geometry and Physics.
Lechtenfeld's research is focused on string theory, gauge theory and integrable models. He has published over 200 research papers on mathematical physics, classical and quantum field theory, gravitation, supersymmetry and integrable many-body systems.
Lechtenfeld has a second career in amateur sports. He finished 25 marathons and numerous triathlons (including 11 ironman races) and twice competed in the Ironman World Championship at Hawai'i.
Education
Lechtenfeld was a student of physics and mathematics at University of Bonn. He completed his Diploma degree in 1982 and received his doctoral degree in 1984 from the university.
Career
After his Ph.D., Lechtenfeld became a Research Fellow at CERN from 1985 till 1987. Lechtenfeld then took up the position of a research associate at City College of New York till 1990. For the subsequent two years, he was a Member of the Institute for Advanced Study in Princeton. In 1992, he moved from the US back to Germany and was appointed by the University of Hannover (later renamed Leibniz University) as a professor of theoretical physics.
Lechtenfeld also held administrative appointments. He served as the founding dean of the Faculty of Mathematics and Physics at the university from 2005 till 2007. Between 2007 and 2014, Lechtenfeld was responsible for the Research Area "Space-Time" as a PI at the Cluster of Excellence QUEST. From 2011 till 2018, he headed the Riemann Center for Geometry and Physics. Since 1995 he runs the annual Saalburg Summer School on Foundations and New Methods in Theoretical Physics.
Research
Lechtenfeld has worked on mathematical physics, classical and quantum field theory, gravitation, supersymmetry and integrable many-body systems. A significant part of his research is focused on string theory.
Finite groups, mean fields, and supersymmetry
Lechtenfeld started his research in the early 1980s, with the representation theory of finite subgroups of SU(n). After obtaining his physics degree for introducing optimized mean fields for atoms, he discovered during his PhD a systematic construction of the Nicolai map for globally supersymmetric field theories. This allowed for its perturbative diagrammatic computation and established the existence of stochastic variables in certain theories.
35 years later, Lechtenfeld returned to the Nicolai map for supersymmetric Yang–Mills theory with an extension to all critical dimensions and an explicit complete evaluation to third order in the coupling.
String theory
Lechtenfeld has conducted significant research in string theory; after his Ph.D. he started working on this and related research areas in the second half of the 1980s. As a postdoc at CERN, Lechtenfeld developed conformal field methods for the computation of superstring scattering amplitudes, refining the bosonized vertex operator construction and applying it to four- and six-fermion scattering. After moving to the City College of New York, he pushed this approach to higher loops, including bosonization on higher-genus Riemann surfaces. In particular, he found a new fermionic representation of beta-gamma systems by employing Fay's trisecant identity. He also developed off-shell conformal methods for superstring field theory. Lechtenfeld then worked on random matrix models of two-dimensional quantum gravity, a topic he continued during his membership at the Institute for Advanced Study in Princeton. He applied the semiclassical approach to finite-N matrix models and derived an integral equation for the classical eigenvalue density.
After accepting a full professorship in Hannover, Lechtenfeld focused his research to N=2 fermionic strings in 2+2 spacetime at tree and loop level. He worked out its path-integral quantization, BRST cohomology, nonlocal hidden symmetries and resulting stringy extensions of selfdual Yang–Mills theory and gravity. During the early 2000s, Lechtenfeld researched on superstring field theory, twistor string theory, topological and pure-spinor strings. He obtained exact solutions to Berkovits’ string field theory and combined the Lorentz invariant N=2 string field theory with the twistor description of selfdual Yang–Mills theory.
Between 2007 and 2014, Lechtenfeld investigated heterotic string compactifications with fluxes and fermionic condensates on nearly Kähler, G2 and Sasakian manifolds, to order α’, finding families of non-supersymmetric string vacua.