Pedro Vieira, Perimeter Institute
Integrability in gauge theories and splitting of strings abstract
Harmonic maps in Hyperbolic spaces, that is strings in Anti de Sitter spacetime, are extremely important in physics. According to the AdS/CFT holographic correspondence these string theories are dual to particle theories known as gauge theories. The string dynamics and the gauge theory dynamics are dual to each other. Strings can propagate and they can also split and merge.
The propagation part of the string is governed by the string energy which is one of the conserved charges in the Harmonic map language. In the gauge theory language these energies correspond to the so-called conformal dimensions of the operators.
The splitting of the string is much more dynamical and somehow even more interesting. In string theory we need to consider harmonic maps in a thrice (or more) punctured sphere while from the gauge theory point of view we should study the correlation functions of three (or more) operators. Integrability plays an absolutely central role in these mathematical physics problems as I will discuss.