Spinon bases in supersymmetric CFTs

Abstract

We present a novel way to organise the finite size spectra of a class of conformal field theories (CFT) with N = 2 or (non-linear) N = 4 superconformal symmetry. Generalising the spinon basis of the SU (n) 1 WZW theories, we introduce supersymmetric spinons (φ − , φ + ), which form a representation of the supersymmetry algebra. In each case, we show how to construct a multi-spinon basis of the chiral CFT spectra. The multi-spinon states are labelled by a collection {n j } of (discrete) momenta. The state-content for given choice of {n j } is determined through a generalised exclusion principle, similar to Haldane's 'motif' rules for the SU (n) 1 theories. In the simplest case, which is the N = 2 superconformal theory with central charge c = 1, we develop an algebraic framework similar to the Yangian symmetry of the SU (2) 1 theory. It includes an operator H 2 , akin to a CFT Haldane-Shastry Hamiltonian, which is diagonalised by multi-spinon states. In all cases studied, we obtain finite partition sums by capping the spinon-momenta to some finite value. For the N = 2 superconformal CFTs, this finitisation precisely leads to the so-called M k supersymmetric lattice models with characteristic order-k exclusion rules on the lattice. Finitising the c = 2 CFT with non-linear N = 4 superconformal symmetry similarly gives lattice model partition sums for spin-full fermions with on-site and nearest neighbour exclusion.