Holographic duality and integrability

A Landscape of metastable de Sitter vacua and that the mechanisms of eternal inflation and bubble nucleation can populate the entire Landscape with“pocket universes”. It may exist (Susskind) a holographic dual description of the multiverse in the form of a two dimensional conformal field theory. On the other hand, there is a connection between integrable hierarchies and two-dimensional conformal theories: from the components of the energy-momentum tensor of conformal theories one can construct quantities that satisfy the integrable equations - the zero curvature condition associated with the group SL(2, R) or SL(3, R). (2+1) dimensional zero curvature condition can be obtained from the self-duality condition in 3+3 dimensions, whereas (1 + 1) dimensional integrable models can be obtained from a self-duality condition associated with Yang-Mills field strengths belonging to SL(2,R) in (2 + 2) dimensions. Using the generalised dimensional reduction method of Filanovsky) one can hide two extra time variables and obtain a new form of duality between dS and the Yang- Mills theory. At last, we show that All AKNS hierarchy contain Kadomtsev-Petviashvili equations therefore KP play the fundamental role in this theory.