The Stress Tensor in Quenched Random Systems

The talk describes recent progress in understanding the behaviour of the stress tensor and its correlation functions at a critical point of a generic quenched random system. The topics covered include: (i) the stress tensor in random systems considered as deformed pure systems; (ii) correlators of the stress tensor at a random fixed point: expectations from the replica approach and c-theorem sum rules; (iii) partition function on a torus; (iv) how the stress tensor enters into correlation functions: subtleties with Kac operators. ∗ Talk presented at Workshop on Statistical Field Theory, Como, Italy, June 2001. This talk is about the stress tensor in generic quenched random systems in which we expect the quenched averaged correlation functions to be those of some conformal field theory. Many of the results generalise to arbitrary dimension, but I shall take d = 2 for simplicity. Quenched random systems as deformed pure systems. Consider the quenched random system defined by the action