Gauge Five-brane Solutions of Co-dimension Two in Heterotic Supergravity

We continue to study the BPS gauge five-brane solutions of codimension two in ten-dimensional heterotic supergravity. The geometry including the dilaton and the NS-NS $B$-field are sourced from the monopole chain in $\mathbb{R}^2 \times S^1$. We find that the geometry is asymptotically Ricci flat and the dilaton is no longer imaginary valued. These properties are contrasted with the smeared counterpart discussed in our previous paper. We perform the T-duality transformations of the solution and find that it never results in a non-geometric object.Comment: 24 pages, 4 figures, typos corrected, version published in JHE

On weak interaction between a ground state and a non-trapping potential

We show that ground states of the NLS moving at nonzero speed are asymptotically stable if they either stay far from the potential, or the potential is small, or the ground state has large speed