(Iso)spin from Isospin in Top-Down Holography
Marcelo Oyarzo, Ricardo Stuardo
TL;DR
The paper explores how a non-Abelian Meron gauge field on SU(2) interacts with isometries in holographic setups to realize a diagonal spin-isospin mixing. By uplifting two SU(2)-gauged supergravity solutions on $M_d\times S^{2}$ through 3-spheres, the authors realize a diagonal symmetry between $SO(3)$ on the external sphere and an internal SU(2), yielding both a supersymmetric I-brane on $S^{2}$ and a non-supersymmetric deformation of $\mathrm{AdS}_{5}\times\mathrm{S}^{5}$, with dilaton fluctuations displaying angular-momentum mixing. The analysis of scalar fluctuations on the 7D internal space shows a spectrum organized by the mixed SU(2) symmetries, satisfying the Breitenlohner-Freedman bound, and exhibiting mass eigenvalues derived from the Laplacian on the squashed 3-sphere and associated spherical harmonics. These results provide a concrete top-down realization of the spin-from-isospin mechanism in holography and open avenues for further embeddings of diagonal symmetry structures in AdS/CFT contexts.
Abstract
Motivated by the spin from isospin mechanism of Jackiw-Rebbi-Hasenfratz-'t Hooft, we study two SU(2) gauged supergravity solutions of the form $M_{d}\times\text{S}^{2}$ containing non-Abelian hedgehog monopole on the 2-sphere. Due to the presence of the monopole, the SO(3) isometry group of the 2-sphere is not a symmetry of the configuration. Instead, a diagonal combination of the SU(2) gauge and the SO(3) isometry of the 2-sphere is the true symmetry of the configuration. Uplifting the solutions to Type II, the gauge-isometry diagonal symmetry becomes a diagonal combination between the SO(3) symmetry of the 2-sphere and a SU(2) symmetry of a 3-sphere used to uplift the configuration. One of the uplifts is supersymmetric and corresponds to the I-brane theory on a 2-sphere. The second background is a deformation of $\text{AdS}_{5}\times\text{S}^{5}$ and is not supersymmetric. We study dilaton fluctuations on the later geometry. Due to the diagonal symmetry, the fluctuations show angular momentum mixing between the SU(2) and SO(3) spins, mimicking the spin from isospin mechanism.