Instantons and the Large N=4 Algebra

TL;DR

This paper explores the geometry of instanton moduli spaces on S^3 x S^1 and suggests a sigma-model with large N=4 superconformal symmetry that may be dual to Type IIB string theory on a specific AdS_3 background.

Contribution

It extends previous results by analyzing the moduli space geometry and proposes a duality between a sigma-model with large N=4 symmetry and Type IIB superstring theory.

Findings

The sigma-model's central charges match duality expectations.

The moduli space is parametrized by three integers related to brane charges.

The model is weakly coupled at large level, supporting the duality hypothesis.

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.