Joint Theoretical High Energy and Discovery Seminar – University of Copenhagen

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Joint Theoretical High Energy and Discovery Seminar

Speaker: Jørgen Rasmussen, University of Queensland

Title: How to arrange dominoes using quantum numbers,


We consider domino tilings of square lattices on rectangles,
cylinders and tori. Working with Lieb's transfer matrix, we
point out that the full set of domino configurations may be
partitioned into disjoint subsets (sectors) closed under the
action of the transfer matrix. These sectors are labelled by
an integer or half-integer quantum number we call the variation
index. In the continuum scaling limit, each sector gives
rise to a representation of the Virasoro algebra. We discuss
the corresponding partition functions and how similarities with
the critical dense polymer model yield natural finitizations
by means of physical combinatorics. These similarities also
indicate an intriguing link to the Ramond and Neveu-Schwarz
sectors of the critical dense polymer model as described by a
conformal field theory with central charge c=-2.