Second-quantized mirror symmetry

We propose and give strong evidence for a duality relating Type II theories on Calabi-Yau spaces and heterotic strings on K3 × T2, both of which have N = 2 spacetime supersymmetry. Entries in the dictionary relating the dual theories are derived from an analysis of the soliton string worldsheet in the context of N = 2 orbifolds of dual N = 4 compactifications of Type II and heterotic strings. In particular we construct a pairing between Type II string theory on a self-mirror Calabi-Yau space X with h11 = h21 = 11 and a (4, 0) background of heterotic string theory on K3 × T2. Under the duality transformation the usual first-quantized mirror symmetry of X becomes a second-quantized mirror symmetry which determines nonperturbative quantum effects. This enables us to show that the quantum moduli space for this example agrees with the classical one. Mirror symmetry of X implies that the low-energy N = 2 gauge theory is finite, even at enhanced symmetry points. This prediction is verified by direct computation on the heterotic side. Other branches of the moduli space, which are not finite N = 2 theories, are connected to this one via black hole condensation.