Gravity theories with negative cosmological constant in three
dimensions (such as AdS3) play 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. This duality naturally emerges in string theory
too, for instance as the near horizon limit of a system of
D1/F1-strings and D5/NS5-branes and was much studied in the early days
of the Maldacena correspondence.
Recently, the interest in Ad3/CFT2 was revived when Babichenko,
Stefanski and Zarembo showed that the maximally super-symmetric AdS3
backgrounds yield classically integrable string non-linear sigma
models. It is natural to ask whether the S-matrix integrability
approach, which works beautifully for the planar limit of AdS5/CFT4,
can be applied here as well. The answer did not appear to be
straightforward, due to several new features and some conceptual
complications of AdS3/CFT2, and indeed eluded us for four years.
In my talk I will provide substantial evidence for an affirmative
answer. To do this, I will discuss in detail the simplest case of
superstrings on AdS3xS3xT4, argue how the same approach can be
extended to more general cases, and describe the exciting future
directions for this integrability program.