Non-Abelian k -vortex dynamics in 𝒩 = 1* theory and its gravity dual

  • Auzzi R
  • Kumar S
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Abstract

We study magnetic flux tubes in the Higgs vacuum of the N=1^* mass deformation of SU(N_c), N=4 SYM and its large N_c string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all N_c we identify a "colour-flavour locked" symmetry, SO(3)_{C+F} which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a Z_{N_c}-valued magnetic flux, with winding, 0 < k < N_c. These k-strings spontaneously break SO(3)_{C+F} to U(1)_{C+F} resulting in an S^2 moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric CP^1 model with a theta angle \theta_{1+1} = k(N_c-k)\theta_{3+1} where \theta_{3+1} is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law T_k \propto k (N_c-k) for large N_c. In the large N_c IIB string dual, the SO(3)_{C+F} symmetry is manifest in the geometry interpolating between AdS_5 x S^5 and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate k-vortices as expanded probe D3-branes formed from a collection of k D-strings. The resulting k-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in N=1^* theory in the large N_c limit.

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Auzzi, R., & Kumar, S. P. (2008). Non-Abelian k -vortex dynamics in 𝒩 = 1* theory and its gravity dual. Journal of High Energy Physics, 2008(12), 077–077. https://doi.org/10.1088/1126-6708/2008/12/077

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