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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 becaptured by a supersymmetric nonlinear sigma model on CP^1 with target spacethe based loop group of SU(k). The ground states, described by L^2-cohomologyclasses, form modules over an affine Lie algebra, while the left-excitedstates, described by chiral differential operators, form modules over atoroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPSsectors of the M5-brane worldvolume theory.

Little Strings, Quasi-topological Sigma Model on Loop Group, and Toroidal Lie Algebras