NS5branes

An NS5-brane is a non-perturbative solitonic five-brane in type II string theories. It carries magnetic charge with respect to the Neveu–Schwarz 2-form B-field, i.e., it is sourced by the NS-NS three-form H = dB. NS5-branes extend along six spacetime dimensions and, as BPS objects, preserve a fraction of supersymmetry. Their tension scales as 1/g_s^2 in string units, reflecting their non-perturbative nature.

Classical solutions in ten-dimensional supergravity describe NS5-branes with a worldvolume along six coordinates and four transverse directions. The metric can be written as ds^2 = η_{μν}dx^μdx^ν + H(r) δ_{ij}dy^i dy^j, with μ = 0,…,5 and i = 1,…,4, where H(r) = 1 + N α'/r^2. The dilaton behaves as e^{2φ} ∝ g_s^2 H(r), and the NS-NS three-form flux through the transverse S^3 carries N units of charge.

In the near-horizon limit r → 0, the throat geometry becomes ds^2 ≈ dx_||^2 + N α' (dr^2/r^2 + dΩ_3^2) and the dilaton runs with the radial coordinate. The three-sphere has radius ~√(N α'). Stacks of NS5-branes give rise to a decoupled, non-gravitational theory on their worldvolume, known as little string theory, which features string-like excitations and holographic descriptions.

NS5-branes are S-dual to D5-branes in type IIB string theory, connecting their physics via dualities. They preserve half of the spacetime supersymmetry (1/2-BPS) and play a central role in discussions of nonlocal six-dimensional theories, holography, and brane constructions in string compactifications.