Fredrik Johansson: The Virasoro algebra and discrete Gaussian free field

Abstract: The Virasoro algebra is a Lie algebra that plays a central role in the Conformal Field Theory methods employed by physicists to describe and study conformally invariant scaling limits of planar critical lattice models from statistical physics. In the talk I will discuss recent joint work with C. Hongler and K. Kytola concerning the discrete Gaussian free field on a square grid. I will explain how for this model discrete complex analysis can be used to construct concrete (exact) representations of the Virasoro algebra of central charge 1 directly on the discrete level.