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AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model

We study dual geometries to a deformed ABJM model with spatially dependent source functions at finite temperature. These source functions are proportional to the mass function $m(x)= m_0 \sin k x$ and its derivative $m'(x)$. As dual geometries, we find hairy black branes and AdS solitons corresponding to deconfinement phase and confining phase of the dual field theory, respectively. It turns out that the hairy AdS solitons have lower free energy than the black branes when the Hawking temperature is smaller than the confining scale. Therefore the dual system undergoes the first order phase transition. Even though our study is limited to the so-called Q-lattice ansatz, the solution space contains a set of solutions dual to a supersymmetric mass deformation. As a physical quantity to probe the confining phase, we investigate the holographic entanglement entropy and discuss its behavior in terms of modulation effect.