The Schrödinger-Virasoro Lie algebra: a mathematical structure between conformal field theory and non-equilibrium dynamics

Jérémie Unterberger (1)

1 IECN - Institut Élie Cartan de Nancy

We explore the mathematical structure of the infinite-dimensional Schrödinger-Virasoro algebra, and discuss possible applications to the integrability of anisotropic or out-of-equilibrium statistical systems with a dynamical exponent $z \neq 1$ by defining several correspondences with conformal field theory.

Mots clés: Schrödinger invariance; Virasoro algebra; non-equilibrium statistical mechanics; vertex algebra; infinite-dimensional Lie algebras; Lie algebra cohomology

Domaines: Physique mathématique [math-ph]

Jérémie Unterberger. The Schrödinger-Virasoro Lie algebra: a mathematical structure between conformal field theory and non-equilibrium dynamics. 2006. ⟨hal-00021041⟩