Abstract
We study the dynamics of probe M5 branes with dissolved M2 charge in bubbling geometries with SO(4) × SO(4) symmetry. These solutions were constructed by Bena-Warner and Lin-Lunin-Maldacena and correspond to the vacua of the maximally supersymmetric mass-deformed M2 brane theory. We find that supersymmetric probe M2 branes polarize into M5 brane shells whose backreaction creates an additional bubble in the geometry. We explicitly check that the supersymmetric polarization potential agrees with the one found within the Polchinski-Strassler approximation. The main result of this paper is that probe M2 branes whose orientation is opposite to the background flux can polarize into metastable M5 brane shells. These decay to a supersymmetric configuration via brane-flux annihilation. Our findings suggest the existence of metastable states in the mass-deformed M2 brane theory.
Highlights
D3 branes into shells of D5 or NS5 branes
We study the dynamics of probe M5 branes with dissolved M2 charge in bubbling geometries with SO(4) × SO(4) symmetry
We focus on the simplest LLM geometry containing dielectric branes, namely the solution corresponding to a single pair of finite-size white and black strips and we consider the dynamics of probe M5 branes within the white strip, i.e. M5 branes wrapping the S3 in the M-theory solution (2.1)–(2.2)
Summary
The full supergravity solutions corresponding to these polarized M5 brane shells for the equal-mass perturbation have been obtained by Bena and Warner in [7] These solutions coincide with the U-duals of the type IIB bubbling geometries constructed by Lin, Lunin and Maldacena in [8], which permit to select boundary conditions that lead to smooth regular solutions. We depict this black and white partitioning of the real line x in figure 1 (b) Such configurations can be obtained from the U-dualization of the type IIB LLM solutions (see appendix A), which are in correspondence with a black and white coloring of a two-plane spanned by coordinates (x1, x2) as shown in figure 1 (a)
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