PARTICLE PHYSICS

With an international conference on “Higher Structures, Moduli Spaces and Integrability”, the Collaborative Research Centre (Sonderforschungsbereich, SFB) of the same name organised by DESY and the University of Hamburg was officially opened at the beginning of April. On this occasion, leading scientists from the field of mathematical physics from all over the world came to Hamburg to discuss the latest developments in algebra and geometry and their connection with quantum field and string theory. Among the more than 150 participants are also many young researchers who have come to Hamburg since the start of the SFB almost a year ago to conduct research on the diverse projects in mathematics and physics. This work on the foundations of the quantum world will initially be funded by the German Research Foundation (DFG) for a period of almost four years.

Further expanding the existing close collaboration between mathematics and physics in Hamburg is a key objective of the new Collaborative Research Centre. “The CRC promotes innovative basic mathematical research that will provide us with new tools for understanding fundamental physical theories,” explains Jörg Teschner, Professor in the Department of Mathematics at the University of Hamburg and researcher in DESY Theory, who submitted the proposal together with a group of 15 colleagues. The research results that the CRC aims to achieve should also contribute to a fundamental understanding of the universe and the phenomena that occur in it, such as the development of black holes, as part of the Cluster of Excellence “Quantum Universe”.

“We are delving deeper into areas of research where maths and physics have reached their limits, with the aim of pushing these limits far beyond,” says Teschner. For example, a new type of mathematics is needed to understand fundamental physical theories of elementary particles such as quantum field theory and string theory in such depth that important features of this world become comprehensible.

The fact that this is often not yet the case is probably not because the existing theories are wrong: “Rather, we do not yet understand the effects predicted by these theories well in many areas,” explains mathematician Teschner, drawing a comparison with meteorology. There, too, the basic equations are known in principle. However, the interactions between the various elements of weather patterns are so complicated that long-term predictions are still not possible today. A similar situation is often found in relation to the fundamental theories of elementary particles.

Researchers from the fields of mathematics and physics at the University of Hamburg and DESY have jointly applied for the new Collaborative Research Centre. Both disciplines expect to benefit greatly from the impetus provided by the other subject. “Questions and ideas from physics provide mathematics with completely new research directions. These should, for example, finally make fundamental aspects of the geometry of complicated three- and four-dimensional spaces comprehensible. On the other hand, physicists need new mathematics in order to understand how nature works at its core,” says Teschner. Another key objective of the Collaborative Research Centre is to promote young scientists. The aim is to further strengthen Hamburg's outstanding international position as a centre for this type of research. DESY theorist Volker Schomerus, who is coordinating the SFB together with Jörg Teschner, sees it as the continuation of a long tradition: “The new SFB is the fruit of a vision that DESY and the University of Hamburg developed 20 years ago to establish mathematical physics with international appeal in Hamburg. At that time, a new working group in string theory was established at DESY and the Hamburg Centre for Mathematical Physics was jointly founded.