Non-geometric Five-branes in Heterotic Supergravity

We study non-geometric five-branes in heterotic supergravity where the first order α′-corrections are present. By performing the α′-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the exotic $5_2^2$-brane solutions associated with the symmetric, the neutral and the gauge NS5-branes. We find that the symmetric $5_2^2$-brane, and the neutral $5_2^2$-brane at $O\left({\alpha }^{{}^{\prime }}\right)$, are T-folds while the gauge $5_2^2$-brane is not a T-fold. This proceeding is based on the work [1] where the details that are omitted in this manuscript are found. (paper)