  In this note, we show that the noncovariant metric boundary term obtained
from the nonlinear sigma model worldsheet derivation of the bulk off-shell
sphere partition function is closely related to the Einstein boundary term in
the Gamma-Gamma noncovariant action. In fact, when expressed in terms of the
trace of the extrinsic curvature tensor, we illustrate that this boundary term
has one-half the coefficient of the Gibbons-Hawking-York boundary term required
such that the total (bulk plus boundary) off-shell classical action has a
well-posed variational principle with Dirichlet boundary conditions.
