Instantons and the Large N=4 Algebra

Abstract

We investigate the differential geometry of the moduli space of instantons on S^3 x 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 x S^3 x S^3 x 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.