The wall of the cave

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang Mills theories must be described by the non-critical strings in the five dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang-Mills theories. The article is written on the occasion of the 40-th anniversary of the IHES.Comment: 18 pages, Late

Supermagnets and Sigma models

We discuss new methods for non-compact sigma models with and without RR fluxes. The methods include reduction to one dimensional supermagnets, supercoset constructions and supertwistors. This work is a first step towards the solution of these models, which are important in several areas of physics. I dedicate it to the memory of Volodya Gribov.Comment: 22 page