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Spin Chain |
Scientists at the Max Planck Institute for Gravitational Physics are currently working hard on the development of a novel approach to gauge field theories and strings. The first class of theories form the cornerstone of our mathematical understanding of the standard model of particle physics. The new methods employ long-range integrable spin chains and, as an added benefit, also lead to deep insights into superstring models. Many researchers believe that the latter are highly relevant in the yet-to-be-built theory of quantum gravity, which should unify the standard model (a quantum theory) with general relativity (a classical theory). String Theories are mysterious in that we have much evidence that they "exist", but we are currently unable to define them in a mathematically precise, non-perturbative way. In particular, it is not known whether seemingly smooth strings are actually made of small discrete building blocks, often called "string bits".
To approach this question of principle, it is sometimes helpful to place the strings into a, as compared to the real world, simplified environment, termed background. A particularly symmetric and beautiful background is the space AdS5 x S5, which is the mathematical abbreviation for a five-dimensional cone (Anti-DeSitter space), with pointwise attachments of five-dimensional spheres - recall that superstrings need to live in an effective number of ten dimensions. It had been conjectured a few years ago that for strings moving in this idealized space an alternative, dual description by a gauge field theory exists. If true, this promises to provide deep insights into the question whether strings are composed of string bits.
And indeed, spectacular, successful tests of this conjectured dual description have recently been performed, many of them in Potsdam-Golm. Much of the progress is due to the discovery of the mentioned spin chain picture of string and gauge theory. Spin chains (see the artist’s impression in the figure) were introduced in 1928 by Heisenberg as a simple one-dimensional model for the quantum theory of metals. Their integrability, meaning exact solvability, was discovered in 1931 by Hans Bethe. They remain of crucial importance in theoretical solid state physics. Their appearance in a completely different area of physics, quantum gravity, is startling and exciting. It seems that we are moving closer to understanding the building blocks of string theories.
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