Instantons and the large N = 4 algebra

We investigate the differential geometry of the moduli space of instantons on S 3 × S 1 . Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N = 4 superconformal symmetry, supporting speculations that this sigma-model may be dual to Type IIB superstring theory on AdS 3 × S 3 × S 3 × S 1 . The sigma-model is parametrized by three integers—the rank of the gauge group, the instanton number, and a ‘level’ (the integer coefficient of a topologically nontrivial B-field, analogous to a WZW level). These integers are expected to correspond to two five-brane charges and a one-brane charge. The sigma-model is weakly coupled when the level, conjecturally corresponding to one of the five-brane changes, becomes very large, keeping the other parameters fixed. The central charges of the large N = 4 algebra agree, at least semiclassically, with expectations from the duality.