Towards integrability for AdS3/CFT2

Gravity theories on 3-dimensional anti-de Sitter (AdS3) played an important role in the understanding of black hole physics, and provided an early example of holography. Their dual 2-dimensional conformal field theories (CFT2) are quite special, since they enjoy (suitable super-symmetric extensions of) Virasoro symmetry.

Recently, the interest in this duality was revived when Babichenko, Stefanski and Zarembo showed that the maximally super-symmetric AdS3 backgrounds yield classically integrable string non-linear sigma models.

I will review the progress in establishing quantum integrability for the planar sector of these string theories, with particular emphasis on the AdS3xS^3xT^4 case, for which the all-loop worldsheet S matrix was recently determined.

I will also discuss more general backgrounds, as well as possible developments including the ones related to black-hole physics, to the study of dual CFT2s, and to higher-spin theories.