Second-Quantized Mirror Symmetry

TL;DR

This paper introduces a duality linking Type II and heterotic string theories on specific Calabi-Yau and K3×T^2 backgrounds, revealing a second-quantized mirror symmetry that computes exact quantum moduli spaces and predicts finiteness of certain gauge theories.

Contribution

It establishes a second-quantized mirror symmetry duality between Type II and heterotic strings, enabling exact calculations of quantum moduli spaces and revealing finiteness properties of N=2 gauge theories.

Findings

Duality relates Type II on Calabi-Yau to heterotic on K3×T^2.

Second-quantized mirror symmetry determines nonperturbative quantum effects.

Low-energy N=2 gauge theory is finite at enhanced symmetry points.

Abstract

We propose and give strong evidence for a duality relating Type II theories on Calabi-Yau spaces and heterotic strings on $K3 \times T^2$, 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 $h^{11}= h^{21}= 11$ and a $(4,0)$ background of heterotic string theory on $K3\times T^2$. 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 compute the exact quantum moduli space. 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, and corresponding dual pairs which are not finite $N=2$ theories, are connected to this one via black hole condensation.