HET seminar: Ara Sedrakyan
Speaker: Ara Sedrakyan
Title: Plateau transitions in quantum Hall effect: link to non-critical string theory
Abstract: Recent results for the critical exponent of the localization length at the integer quantum Hall transition differ considerably between experimental (ν ≈ 2.38) and numerical (ν ≈ 2.6) values obtained in simulations of the Chalker-Coddington (CC) network model. We propose a mechanism that changes the value of ν even within the single-particle picture. We revisit the arguments leading to the CC model and consider more general networks with structural disorder. Numerical simulations of the new model lead to the value ν ≈ 2.37.
We argue that in a continuum limit the structurally disordered model maps to free Dirac fermions coupled to U(1) gauge filed but also to quenched two-dimensional quantum gravity. As such the model becoming kind of non-critical string theory but with total central charge of matter fields C>1. Hence, the model shows existence of string theories beyond c=1 barrier.
We formulate matrix model which will reproduce the physics of this type of models.
Moreover, formulated matrix model can describe string theories corresponding to any
integrable model living on fluctuating surfaces.