This is an elementary question in string theory. In Polyakov action, it is often explained that worldsheet metric is independent dynamic variable and target manifold often (though it does not have to be) is a Minkowski one.
Intuitively, we think of strings in worldsheet sweeping through the submanifold of the target spacetime - and that means that once target manifold is set, then what we actually describe should follow the metric tensor of the target manifold.
So what does metric tensor of worldsheet actually do to change our descriptions of physics? Is it that it contributes additional metric tensor term to the background manifold metric tensor?
Or does this mean that metric tensor in worldsheet "fluctuates" relative to target manifold's metric tensor, or what?