Integrability in the AdS/CFT correspondence – University of Copenhagen

Integrability in the AdS/CFT correspondence

The AdS/CFT correspondence provides a framework in which quantum field theory and string theory constitute equivalent descriptions of the same system. In its pure form the AdS/CFT correspondence involves a supersymmetric and conformal quantum field theory (CFT) and a likewise supersymmetric string theory which lives in a 10-dimensional space consisting of a five-dimensional sphere and a five-dimensional anti-de-Sitter (AdS) space.

The problem of determining the spectrum of the excitations of the pure AdS/CFT system in the so-called planar limit has proven to be exactly solvable and identical to the spectral problem of a certain long-range integrable spin chain. Accordingly, the quantum field theory and the string theory are to be viewed as nothing but two limits of the same long-range integrable spin chain.

Our group works on extending the the integrability techniques to observables which are not captured by the spectral problem such as three-point functions and form factors and on going beyond the planar limit. 

Furthermore, we are investigating less symmetric versions of the AdS/CFT set-up, in particular set-ups which involve defects in the quantum field theory and higher dimensional objects, so-called probe branes, in the string theory. Our focus for these less symmetric set-ups has so far been on one-point functions and Wilson loops.

Illustration of the defect set-up. (a) String theory side: k out of N D3 branes end on a probe D5-brane, (b) Field theory side: the defect separates two regions with different rank of the gauge group.