Exact Four-Parameter Rotating NS--NS Vacuum in Double Field Theory
Abstract
We construct an exact rotating vacuum of the NS--NS sector, equivalently a Double Field Theory vacuum. The construction applies compact SO(2) S-duality to a rotating Einstein--scalar seed. The solution has four independent parameters {m,j,q,ζ}. To our knowledge, this is the first explicit rotating solution of the pure NS--NS vacuum equations with all three NS--NS fields {g,B,ϕ} determined analytically, independent dilaton and H-flux charges, and no Maxwell sector. The static limit is obtained by taking the rotation parameter j→ 0. In this limit the geometry is not the spherical Burgess--Myers--Quevedo solution. Instead, it is an axial Zipoy--Voorhees branch carrying H-flux, so an oblate deformation remains after rotation is switched off. This geometric memory is absent in pure general relativity and in Einstein--Maxwell--dilaton--axion. The two static branches nevertheless share the same ℓ=0 parametrized post-Newtonian data {MG,βPPN,γPPN,h}. They give two inequivalent NS--NS geometries at identical monopole charges, with the degeneracy lifted at ℓ=2. At the Kerr horizon locus the outer shell is generically singular in curvature. Above the threshold |q|>√(m2−j2), polar geodesics are repelled outward and the rotation axis becomes regular in curvature at the shell. On that axis the inverse metric gμν stays finite while the lower-index Riemannian metric components diverge, whereas off the axis the inverse metric itself diverges. This axis-local degeneracy may offer a setting for non-Riemannian geometry in Double Field Theory, where gμν is not fundamental and the O(D,D) variables {d,ℋAB} remain well defined.
Versions
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BibTeX
@misc{jang2026exact,
title = {{Exact Four-Parameter Rotating NS--NS Vacuum in Double Field Theory}},
author = {Hun Jang and Minkyoo Kim and Jeong-Hyuck Park},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.08889},
eprint = {2606.08889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.08889},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Exact Four-Parameter Rotating NS--NS Vacuum in Double Field Theory
AU - Hun Jang
AU - Minkyoo Kim
AU - Jeong-Hyuck Park
PY - 2026
DA - 2026/08/10
PB - arXiv
DO - 10.48550/arxiv.2606.08889
UR - https://arxiv.org/abs/2606.08889
AB - We construct an exact rotating vacuum of the NS--NS sector, equivalently a Double Field Theory vacuum. The construction applies compact SO(2) S-duality to a rotating Einstein--scalar seed. The solution has four independent parameters {m,j,q,ζ}. To our knowledge, this is the first explicit rotating solution of the pure NS--NS vacuum equations with all three NS--NS fields {g,B,ϕ} determined analytically, independent dilaton and H-flux charges, and no Maxwell sector. The static limit is obtained by taking the rotation parameter j→ 0. In this limit the geometry is not the spherical Burgess--Myers--Quevedo solution. Instead, it is an axial Zipoy--Voorhees branch carrying H-flux, so an oblate deformation remains after rotation is switched off. This geometric memory is absent in pure general relativity and in Einstein--Maxwell--dilaton--axion. The two static branches nevertheless share the same ℓ=0 parametrized post-Newtonian data {MG,β_PPN,γ_PPN,h}. They give two inequivalent NS--NS geometries at identical monopole charges, with the degeneracy lifted at ℓ=2. At the Kerr horizon locus the outer shell is generically singular in curvature. Above the threshold |q|>√(m^2−j^2), polar geodesics are repelled outward and the rotation axis becomes regular in curvature at the shell. On that axis the inverse metric g^μν stays finite while the lower-index Riemannian metric components diverge, whereas off the axis the inverse metric itself diverges. This axis-local degeneracy may offer a setting for non-Riemannian geometry in Double Field Theory, where g_μν is not fundamental and the O(D,D) variables {d,ℋ_AB} remain well defined.
ER -