Quasi-particles in conformal field theoryThis paper was presented at the Theory CANADA 4 conference, held at the Centre de Recherches Mathématiques at the Université de Montréal, Québec, Canada on 4–7 June 2008.
After recalling some basing features of conformal field theory, we present an elementary introduction to the description of the states in the irreducible modules of the minimal models. The characters, which encode the state content of each module, are easily constructed from the representation theory of the Virasoro algebra and they take the form of infinite alternating sums. On the other hand, the relation between the minimal models and particular statistical models has led to the discovery of alternative expressions for the characters, which are positive definite. These entail a (yet to be fully worked out) quasi-particle description of the space of states, via a filling process with restrictions akin to the exclusion principle. The simplest class of positive characters, pertaining to the ℳ(2,p) models, is presented, and its underlying combinatorial aspects are spelled out. A natural conformal field theoretical interpretation of its quasi-particles is presented.