Integrability and Gauge/String Duality

[RG # 131] Integrability and Gauge/String Duality

March 1 - May 31, 2012

Matthias Staudacher (Humboldt-University, Berlin)
Romuald Janik (Jagiellonian University)

The focus of the group is on a currently intensively-studied model in theoretical physics, which has been termed by some the "hydrogen atom of the 21st century". The basic idea and goal was to construct a mathematically exact solution of an, admittedly idealized, quantum field theory of the general type as occurs in the description of the forces between our universe's elementary particles, with the notable exception of the gravitational force.

Yang-Mills gauge theory is named for its inventors, Chen Ning Yang and Robert Mills. The word gauge refers to the fact that at the heart of these theories lies a certain built-in redundancy in its mathematical description very hard to eliminate, while apparently necessary in order to properly record and understand the rules of the game. The idealized system at the focus of our group is called N=4 super Yang-Mills gauge theory. It stipulates that in addition to our standard continuous ("bosonic") spacetime dimensions, certain hidden discrete ("fermionic") dimensions exist. The number N=4 refers to the fact that this model has four such curious symmetries.

The N=4 gauge model is the most beautiful and simplest Yang-Mills theory one can come up with, even though it certainly does not directly appear in nature. It is also a deeply mysterious model, and it has become clear in recent years that it possesses further hidden symmetries as well as seemingly contradictory, alternative descriptions, which promise to allow for a complete solution of the model, at least for certain quantities and in certain limits. This is precisely what we are setting out to achieve with our program at the IIAS.