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One-loop effective brane action

The one-loop effective action for a $p$ brane embedded in a $D=p+2$ Minkowski spacetime in the static gauge is calculated. Rescaling the quantum fluctuation by $\sqrt{-g_0}$ evaluated on the background brane leads to the one-loop effective action expressed only in terms of infrared and ultraviolet divergent geometric scalars. After the infrared divergences are absorbed into the quantum fluctuation, there remains the finite number of ultraviolet divergences. This implies that the $D=p+2$ Poincaré symmetry and the $D=p+1$ general coordinate invariance are preserved in one-loop order.