Non-geometric Five-branes in Heterotic Supergravity

TL;DR

This paper investigates T-duality transformations of heterotic five-branes with $oldsymbol{ ext{alpha'} }$-corrections, revealing non-geometric T-fold structures and novel space-time features of exotic brane solutions.

Contribution

It provides the first analysis of $oldsymbol{ ext{alpha'} }$-corrected T-duality chains for heterotic five-branes, uncovering their non-geometric and exotic properties.

Findings

The symmetric $oldsymbol{5^2_2}$-brane is a T-fold with non-geometric features.

The neutral $oldsymbol{5^2_2}$-brane is a T-fold at $oldsymbol{ ext{O}( ext{alpha'})}$ order.

The gauge $oldsymbol{5^2_2}$-brane exhibits unusual space-time structures, not classified as a T-fold.

Abstract

We study T-duality chains of five-branes in heterotic supergravity where the first order $\alpha'$-corrections are present. By performing the $\alpha'$-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and the exotic $5^2_2$-brane solutions associated with the symmetric, the neutral and the gauge NS5-branes. We find that the Yang-Mills gauge field in these solutions satisfies the self-duality condition in the three- and two-dimensional transverse spaces to the brane world-volumes. The $O(2,2)$ monodromy structures of the $5^2_2$-brane solutions are investigated by the $\alpha'$-corrected generalized metric. Our analysis shows that the symmetric $5^2_2$-brane solution, which satisfies the standard embedding condition, is a T-fold and it exhibits the non-geometric nature. We also find that the neutral $5^2_2$-brane solution is a T-fold at least at $\mathcal{O} (\alpha')$. On the other hand, the gauge $5^2_2$-brane solution is not a T-fold but show unusual structures of space-time.