Triangle Seminars

Abstract:
In this seminar we will look at two places where two-dimensional conformal field theory is related to the study of matrix models. The first is that a matrix model may be thought of as a statistical model on a fluctuating lattice. In the continuum limit, that is in the limit of large matrix size N, this yields a c less than 1 CFT coupled to gravity. The second relation is that the matrix model can, even before the continuum limit, be described in terms of free bosons. The free boson CFT turns out to be useful in understanding the large N behaviour of the matrix model.

Abstract:
In recent years it has been realized that Hermiticity of the Hamiltonian is not a necessary condition for the reality of its eigenvalues. In many cases it is sufficient for the Hamiltonian to have an unbroken PT symmetry, but the natural Hilbert-space metric of such theories is not positive definite, which raises severe problems as to their physical interpretation. However, it turns out to be possible to construct another,dynamically-determined, metric eta=exp(iQ) that is indeed positive definite. For the most part Q can only be constructed perturbatively,but there are some cases where it is known exactly. With the aid of Q one can construct an equivalent Hermitian Hamiltonian, which, however, may be rather complicated and non-local.