# 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=mc^{2} 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.