Quantum gravity corrections to the Schwarzschild mass

Vacuum spherically symmetric Einstein gravity in $N>~4$ dimensions can be cast in a two-dimensional conformal nonlinear sigma model form by first integrating on the $\left(N-2\right)$-dimensional (hyper)sphere and then performing a canonical transformation. The conformal sigma model is described by two fields which are related to the Arnowitt-Deser-Misner (ADM) mass and to the radius of the $\left(N-2\right)$-dimensional (hyper)sphere, respectively. By quantizing perturbatively the theory we estimate the quantum corrections to the ADM mass of a black hole.