# Conference “Integrability in Gauge and String Theory” from 24th to 28th July 2006 at the Albert Einstein Institute

Can strings also be particles?

The physicists' search for a grand unified theory encounters hard conceptual and mathematical limits in their attempt to reconcile gravity and quantum theory. This is to be overcome with the help of string theory.

String theory is the most important candidate for a theory that combines Einstein's general theory of relativity with quantum mechanics and the standard model of elementary particles. It is based on the assumption that the smallest building blocks of matter are one-dimensional threads (strings). Like strings that are made to vibrate and produce different sounds, the vibrations of the strings correspond to the different elementary particles.

"However, the question remains open as to what exactly a string really is," says Matthias Staudacher, string theorist at the MPI for Gravitational Physics (Albert Einstein Institute, AEI) and one of the conference organizers. "The current debate is whether strings can be made up of particles and vice versa. It is also still unclear what these particles could look like." It is becoming increasingly clear that a mathematical method developed by Hans Bethe in the early days of quantum mechanics - the "Bethe approach" - plays a decisive role in the investigation of string and particle models.

In 1928 Heisenberg introduced the so-called "spin chains" into theoretical physics. In 1931 Hans Bethe discovered that these one-dimensional models for metals can be solved exactly. This "Bethe approach" thus goes back directly to the origins of quantum mechanics. Since then, it has played an important role in the mathematical understanding of complicated physical phenomena such as high-temperature superconductivity, the theory of defects in solids and the quantum hall effect. Over the past four years, it has been discovered that Bethes' mathematical method also applies to certain string and particle models, which can be studied extremely efficiently.

"It is particularly gratifying that a large part of the current discoveries have been made through the successful collaboration of physicists working in Europe, and that the EU's investments in European research networks are bearing visible fruit," said Matthias Staudacher.

## String theories - What exactly is a string?

are currently the world's preferred models for answering one of the "final questions" of fundamental physics: How exactly does one unite Einstein's theory of relativity with quantum mechanics and the standard model of elementary particles? In principle, this unification is achieved by the strings, but the exact definition of these theories remains mysterious. The question of what exactly a string really is also remains open. In order to get closer to the mystery of strings, it makes sense to study their motion in a highly idealized environment compared to the real world. A particularly symmetrical and mathematically suitable environment is based on the curved Anti-de Sitter Space (AdS), which also plays an important role in cosmological models. Almost ten years ago, the astonishing assumption was made that in this case a dual description by a particular supersymmetric particle model would be possible. So can strings also be particles in the context of this duality called "AdS/CFT correspondence" and vice versa?

This particle theory, the "maximum supersymmetric gauge theory", is in turn an idealised version of precisely those theories that make up the so successful Standard Model of elementary particles, which has been experimentally verified with great accuracy. If there is a connection with the strings, there are many possibilities to use our extensive knowledge in particle physics to track down the strings. Conversely, we can also hope to use the strings to develop new methods of investigation for the mathematically extremely complicated particle theories, and especially for the theory of the strong nuclear forces. Because: Despite the great successes in calculating the experimental consequences of the Standard Model, many questions remain open at present where the mathematical methods available to date fail completely.

The string theorists' current research work will possibly also make significant contributions to the evaluation of the experiments at the LHC (Large Hadron Collider), which is expected to go into operation in Geneva in 2008 and deliver initial results in 2009.

## The "Bethe approach" in string theory and particle physics

The discovery of Bethes integrable structures in this field of tension between strings and particles is therefore an unexpected gift, and the conference at the Albert Einstein Institute aims to make interdisciplinary use of the consequences of the resulting new computing methods. In particular, one may now hope for constructive proof of the AdS/CFT correspondence in the near future, with the implications already mentioned for our understanding of the fundamental interpretation of strings, as well as for the development of new quantitative methods for the analysis of the theoretical components of the Standard Model of elementary particle physics. Furthermore, it cannot be excluded that the discovery of Bethes soluble structures in the field of high-energy physics will ultimately benefit solid state physics again. One reason for this hope is the extremely subtle and beautiful symmetries derived from string and gauge theory, which have so far been overlooked in solid state theory.

## International Cooperation/European Networks on String Theory

The field discussed at the AEI within the framework of the conference is an outstanding example of excellent basic research in Europe: The novel applicability of the "Bethe approach" is being researched across disciplinary boundaries, especially in European collaborations - they are world leaders in this field. In addition to the Potsdam AEI, the formal and informal research networks include the University of Uppsala/Sweden, ENS Paris/France, Universidad Autonoma Madrid/Spain, Niels Bohr Institute Copenhagen/Denmark and the University of Krakow/Poland. The importance of this dynamic field of research is also underlined by the European Union, which, among other things, supports the "Superstring Theory" and "Forces Universe" networks, which serve in particular to train young researchers (doctoral and post-doctoral students) in this exciting field of research. Nevertheless, leading American theorists, such as the "string guru" Joseph Polchinski from Santa Barbara (California) and Nikolai Reshetikhin (Berkeley/California, Humboldt Award Winner and currently a visiting scholar at the AEI) will of course also be taking part in the Potsdam Conference.