U-branes and T^3 fibrations

TL;DR

This paper constructs eight-dimensional vacuum solutions with U-duality symmetries, focusing on SL(3,Z) properties, and explores their connection to Calabi-Yau mirror symmetry through T^3 fibrations.

Contribution

It introduces a class of fivebrane solutions on lines in a three-dimensional base, leading to U-manifolds with Ricci-flat Kähler metrics linked to T^3 fibered Calabi-Yau threefolds.

Findings

Constructed fivebrane solutions with SL(3,Z) symmetry.

Established a connection between U-manifolds and Calabi-Yau mirror symmetry.

Provided a framework for studying T^3 fibrations in string theory.

Abstract

We describe eight-dimensional vacuum configurations with varying moduli consistent with the U-duality group $SL(2,Z) \times SL(3,Z)$. Focusing on the latter less-well understood SL(3,Z) properties, we construct a class of fivebrane solutions living on lines on a three-dimensional base space. The resulting U-manifolds, with five scalars transforming under SL(3), admit a Ricci-flat Kahler metric. Based on the connection with special lagrangian $T^3$ fibered Calabi-Yau 3-folds, this construction provides a simple framework for the investigation of Calabi-Yau mirrors.