  We consider a new action of a two-dimensional field theory interacting with
gravitational field. The action is interpreted as the area of a surface
imbedded into four-dimensional Mincowski target space. In addition to
reparametrization invariance the new action has one extra infinite-dimensional
local symmetry with a clear geometrical meaning. The special gauge choice,
which includes the gauge condition of tracelessness of the energy-momentum
tensor, leads to an effective free scalar field theory. The problem of
anomalies in quantum theory and possible connection with matrix quantum
mechanics are also discussed.
