Ground States of Duality-twisted Sigma-Models with K3 Target Space

TL;DR

This paper studies the ground states of a duality-twisted sigma-model with an elliptically fibered K3 target space, revealing contributions from cohomological states and localized states at singular fibers, with implications for geometric quantization.

Contribution

It introduces a novel analysis of ground states in duality-twisted sigma-models on K3, connecting cohomology, localization, and geometric quantization.

Findings

Witten index includes contributions from cohomology and localized states.

States localized at singular fibers significantly affect the ground state structure.

Discussion of orbifold limits and geometric quantization links.

Abstract

We analyze the ground states of a two-dimensional sigma-model whose target space is an elliptically fibered K3, with the sigma-model compactified on a circle with boundary conditions twisted by a duality symmetry. We show that the Witten index receives contributions from two kinds of states: (i) those that can be mapped to cohomology with coefficients in a certain line bundle over the target space, and (ii) states whose wave-functions are localized at singular fibers. We also discuss the orbifold limit and possible connections with geometric quantization of the target space.