Is the idea of integrability the key to “what keeps the world together at its core”?
When physicists find something “attractive”, it usually signifies something of special importance - because “attractive”, especially conclusive and clearly formulated theories, often prove to also be groundbreaking. Albert Einstein’s E=mc2 is a good example of this. Internationally, the idea of “integrability”, which harks back to the “Bethe Ansatz” developed by Hans Bethe 78 years ago, is just such an “attractive” phenomenon. And it could prove to be the key to the so-called “theory of everything”. Around 140 top scientists from all over the globe will therefore meet for the conference “Integrability in Gauge and String Theories” at the Potsdam-based Max Planck Institute for Gravitational Physics (Albert Einstein Institute/AEI) to discuss current approaches and developments. The reason: Integrability could provide answers to one of the most fundamental issues facing modern physics: How can the general theory of relativity be unified with quantum mechanics - or, what holds the world together at its core?
Integrability is a phenomenon that is normally limited to one- or two-dimensional systems. However, it was recently discovered that higher dimensional quantum field theories can also be integrable. The resulting structures, such as factorized S-matrices, Bethe equations, the thermodynamic Bethe Ansatz, as well as quantum algebra, have numerous similarities with already known solution models (e.g. Heisenberg magnets, Hubbard models), but require an insight that must still be further deepened.
Participants and conference agenda
Around 140 solid-state, particle and string theoreticians from all over the world will focus on one of the most exciting issues in theoretical high-energy physics. During the course of last year, it was revealed that the “Bethe Ansatz”, already discovered 78 years ago by Hans Bethe, could be the key to “what holds the world together at its core”.
String theory is the most important candidate for a theory that could unify 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 components of matter are one-dimensional strings. Just as strings that are made to vibrate generate sounds, the vibration of the strings here corresponds to the various elementary particles.
Currently under discussion is whether strings can be formed from particles and vice versa. It is still unclear what these particles might look like. It is becoming clear that the mathematical method, which was already developed by Hans Bethe during the time of origin of quantum mechanics - the “Bethe Ansatz” - plays a decisive role in the research of string and particle models.
String theories are currently the preferred models throughout the world for clearing up one of the “last open questions” of fundamental physics: How can Einstein’s relativity theory be reconciled with quantum mechanics and the Standard Model of elementary particles? This unity can be attained through the strings; however, the exact definition of these theories remains mysterious. The question as to exactly what a string really is also remains unanswered. In order to gain a better understanding of the secret of strings it is perhaps a good idea to take a look at their movement in an idealized environment in contrast to the real world. A particularly symmetrically and mathematically suitable environment is based on the curved Anti-de-Sitter Space (AdS), which also plays an important role in cosmological models. Around ten years ago, the astounding assumption was proposed that in this case a dual description through a specific super-symmetrical particle model was possible. Could strings actually be, within the framework of this “AdS/CFT-Correspondence” as the duality is called, also particles and vice versa?
This particle theory, the “maximum super-symmetrical gauge theory”, is in turn an idealized version of exactly those theories that define the Standard Model of elementary particles which have been verified so successfully and with great precision. If there actually is a coherency with the strings this would open up manifold possibilities to make use of our extensive knowledge in particle physics to track down the strings. Conversely, we can also hope that, with the help of the strings, new research methods can be developed for the mathematically extremely difficult particle theories and, especially, for the theory of strong nuclear force. The reason: Despite great success in the computation of experimental consequences of the Standard Model, there are still many open questions that cannot be answered at all through the currently available mathematical methods.
The “Bethe Ansatz” in string theory and particle physics - overseen symmetries
The discovery of Bethe’s integrable structures at this interface of strings and particles is thus an unexpected gift - and the conference at the Albert Einstein Institute has set itself the goal to use the consequences of the resulting new computing methods in an interdisciplinary manner. In particular, one can hope for, in the near future, constructive proof of the AdS/CFT- Correspondence with the already mentioned ramifications for our understanding of the fundamental interpretation of strings, as well as for the development of new quantitative methods for analyzing the theoretical components of the Standard Model of elementary particle physics. Moreover, it cannot be ruled out that the discovery of Bethe’s solvable structures in high-energy physics will also ultimately prove advantageous for solid state physics. Cause for hope in this respect is provided by the extremely subtle and attractive symmetries from the string and gauge theories, which had, to date, been overlooked in the sold-state theory.
International cooperation
The topic that will be discussed at the conference at the AEI, is an outstanding example of excellent basic research in Europe: The innovative applicability of the “Bethe Ansatz” is being researched across all disciplinary boarders in European collaborative projects - these are leading the way all over the globe in this area. In addition to the Potsdam-based AEI, the formal and informal research networks include, among other institutions, the University Uppsala/Sweden, the ENS Paris/France, University Utrecht/Netherlands, Trinity College, Dublin/Ireland, the Universidad Autonoma in Madrid/Spain, the Niels Bohr Institute Copenhagen/Denmark and the University Krakow/Poland.
Experts at the AEI
With Niklas Beisert and Matthias Staudacher, two internationally recognized experts for gauge and string theory are based at the AEI. Matthias Staudacher has just received, for his work in this area, the highly respected Academy Prize of the Berlin-Brandenburg Academy of Sciences and Humanities; in 2007, Niklas Beisert was awarded the prestigious Gribov Medal of the European Physical Society.
