Abstract
We study the ground states and left-excited states of the Ak−1N=(2,0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU(k). The ground states, described by L2-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.
Highlights
The Ak−1 N = (2, 0) little string theory can be described as follows
In the very low energy discrete lightcone quantization (DLCQ) limit, the theory on the D-string worldsheet is that of the N = (4, 4) supersymmetric sigma model with target space being the moduli space of SU (k) N -instantons on R4 (denoted as MNSU(k)(R4)) [4,5,6]
We investigate the topological and quasi-topological sectors of this N = (4, 4) supersymmetric sigma model in an attempt to understand the ground states and left-excited states of the little string theory, respectively
Summary
The ground states of the N =(4,4) sigma model with target space MNSU(k)(R4) correspond to the L2-cohomology of MNSU(k)(R4) as local observables [13]. This is equivalent, via Atiyah’s theorem, to the L2-cohomology of M(CP 1 −−N→ ΩSU (k)), which are the hol. Correspond to local observables described by the Cech cohomology of the sheaf of chiral de Rham complex on MNSU(k)(R4) [15, 17] This is equivalent, via Atiyah’s theorem, to the Cech cohomology of the sheaf of chiral de Rham complex on M(CP 1 −−N→ ΩSU (k)), hol. Which are the local observables of the quasi-topological sector of the auxiliary theory defined, which is an N = (2, 2) sigma model with target space M(CP 1 −−N→ ΩSU (k)).
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