  We study the ground states and left-excited states of the A_{k-1} N=(2,0)
little string theory. Via a theorem by Atiyah [1], these sectors can be
captured by a supersymmetric nonlinear sigma model on CP^1 with target space
the based loop group of SU(k). The ground states, described by L^2-cohomology
classes, form modules over an affine Lie algebra, while the left-excited
states, described by chiral differential operators, form modules over a
toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS
sectors of the M5-brane worldvolume theory.
