L6

I will review an elegant, theory-independent argument that proves the existence of exactly marginal operators in the presence of a conformal manifold. The proof relies on a few technical assumptions, which I will discuss in detail. The rest of the discussion will be phrased in terms of conformal interfaces separating two CFTs on the conformal manifold, which we take as an opportunity to discuss the fundamentals of defect CFTs. The overarching topic into which this result fits is that of proving certain (AdS) swampland conjectures from CFT principles.

Given a quantum Hamiltonian, represented as an $N \times N$ Hermitian matrix $H$, we derive an expression for the largest Lyapunov exponent of the classical trajectories in the phase space appropriate for the dynamics induced by $H$. To this end we associate to $H$ a graph with $N$ vertices and derive a quantum map on functions defined on the directed edges of the graph. Using the semiclassical approach in the reverse direction we obtain the corresponding classical evolution (Liouvillian) operator. Using ergodic theory methods (Sinai, Ruelle, Bowen, Pollicott\ldots) we obtain closed expressions for the Lyapunov exponent, as well as for its variance. Applications for random matrix models will be presented.