U-Duality and Integral Structures

TL;DR

This paper explores the U-duality group in type II superstring compactifications on K3 and tori, relating various string theories and supergravity through integral structures linked to quantum cohomology.

Contribution

It establishes a connection between the integral structures in the Ramond-Ramond sector and quantum cohomology, providing a unified framework for analyzing moduli spaces across different theories.

Findings

Identifies the U-duality group structure for compactifications on K3 and tori.

Relates the integral structure in the Ramond-Ramond sector to quantum cohomology.

Provides a unified description of type IIA, IIB, heterotic, and M-theory limits.

Abstract

We analyze the U-duality group for the case of a type II superstring compactified to four dimensions on a K3 surface times a torus. The various limits of this theory are considered which have interpretations as type IIA and IIB superstrings, the heterotic string, and eleven-dimensional supergravity, allowing all these theories to be directly related to each other. The integral structure which appears in the Ramond-Ramond sector of the type II superstring is related to the quantum cohomology of general Calabi-Yau threefolds which allows the moduli space of type II superstring compactifications on Calabi-Yau manifolds to be analyzed.