String Theory Journal Club

I will discuss a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of 2-dimensional σ-models giving rise to integrability-preserving transformations. Assuming a generalised Scherk-Schwarz ansatz, in fact, the two problems admit essentially the same algebraic formulation, emerging from an underlying double Lie algebra. After presenting the derivation of the classification, we discuss in detail the relation to modified supergravity and the additional conditions to recover the standard (unmodified) supergravity. Starting from a master equation - that encodes all the possible continuous deformations allowed in the family of solution-generating techniques - I show that these are classified by the Lie algebra cohomologies H^2(h,R) and H^3(h,R) of the maximally isotropic subalgebra h of the double Lie algebra. Finally, I introduce a non-trivial example, the integrable bi-Yang-Baxter-Wess-Zumino model.