Taub-NUT Crystal

TL;DR

This paper explores periodic arrays of multi-Taub-NUT centers with positive and negative charges, revealing their crystal-like structure, T-duality transformations, and potential for probing singular geometries with gauge theories.

Contribution

It introduces a novel periodic array of Taub-NUT centers including negative charges, analyzes their dualities, and discusses their relevance to heterotic 5-brane backgrounds and gauge theory probes.

Findings

Arrays classified by space groups similar to ionic crystals

T-duality transforms the array into NS5-branes with SU(2) structure

Singular heterotic 5-brane backgrounds can be studied via gauge theories

Abstract

We consider the Gibbons-Hawking metric for a three-dimensional periodic array of multi-Taub-NUT centers, containing not only centers with a positive NUT charge but also ones with a negative NUT charge. The latter are regarded as representing the asymptotic form of the Atiyah-Hitchin metric. The periodic arrays of Taub-NUT centers have close parallels with ionic crystals, where the Gibbons-Hawking potential plays the role of the Coulomb static potential of the ions, and are similarly classified according to their space groups. After a periodic identification and a Z2 projection, the array is transformed by T-duality to a system of NS5-branes with the SU(2) structure, and a further standard embedding yields, though singular, a half-BPS heterotic 5-brane background with warped compact transverse dimensions. A discussion is given of the possibility of probing the singular geometry by two-dimensional gauge theories.