Ultrametric space cut instead of 2d one in 2d quantum field models

Abstract

It is possible to formulate 2d field theory on the ultrametric space with the free correlators identical to 2d correlators and the same potential. Such model should carry some features of original model for scale invariant theories. For the case of strings and 2d conformal models it is possible to derive exact results. It is possible to investigate not only bulk structure (phase transition points) of theory, but sometimes also correlators. Such ultrametric models could be naturally expressed via Random energy model and directed polymer on Cayley tree.