Meaning of area in the Nambu Goto string action

[clerk]

I am confused about what area is being minimised in the nambu goto action..the one in the target space or the one in the parameter space? From Zwiebach's book I think he is trying to construct the area in target space and in the process we get derivatives with respect to parameters since each co-ordinate in the target space is now a function of the two parameters.. But reading David Tong's notes, it seems he is building the area in the worldsheet rather than in target space...because he talks about pullback of the flat minkowskian metric on the worldsheet.. (by worldsheet i think he means the parameter space?)

 

[martinbn]

I think they are doing the same thing. By world sheet Tong means the image, and the pullback of the metric is the restriction to the world sheet. So in both cases it is area in the target space.

 

[tom.stoer]

afaik these two concepts are strictly equivalent in differential geometry