We investigate the brane models in arbitrary dimensional critical gravitypresented in [Phys. Rev. Lett. 106, 181302 (2011)]. For the model of the thinbranes with codimension one, the Gibbons-Hawking surface term and the junctionconditions are derived, with which the analytical solutions for the flat, AdS,and dS branes are obtained at the critical point of the critical gravity. It isfound that all these branes are embedded in an AdS$_{n}$ spacetime, but, ingeneral, the effective cosmological constant $\Lambda$ of the AdS$_{n}$spacetime is not equal to the naked one $\Lambda_0$ in the critical gravity,which can be positive, zero, and negative. Another interesting result is thatthe brane tension can also be positive, zero, or negative, depending on thesymmetry of the thin brane and the values of the parameters of the theory,which is very different from the case in general relativity. It is shown thatthe mass hierarchy problem can be solved in the braneworld model in thehigher-derivative critical gravity. We also study the thick brane model andfind analytical and numerical solutions of the flat, AdS, and dS branes. It isfind that some branes will have inner structure when some parameters of thetheory are larger than their critical values, which may result in resonant KKmodes for some bulk matter fields. The flat branes with positive energy densityand AdS branes with negative energy density are embedded in an $n$-dimensionalAdS spacetime, while the dS branes with positive energy density are embedded inan $n$-dimensional Minkowski one.
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