Action growth rates of black holes in the Chern-Simons modified gravity

Among many modified gravity theories, the Chern-Simons modified gravity stands out as one of the few examples whose Dirichlet boundary problem has been well studied. Known solutions to this theory include the Schwarzschild black hole and a slowly rotating black hole. Making use of the Dirichlet boundary term of this theory, we calculate the late-time action growth rates of the Wheeler-DeWitt patch for the Schwarzschild and the slowly rotating solutions. In light of the conjecture of complexity/action duality, the result has implications on the quantum complexity of a state in the dual field theory.