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I always wondered about the metric to be used in string theory. As 10-4 (11-4) or 26-4 dimensions are supposed to be curled up or being a Calabi-Yau manifold, in this part of the space-time the metric should be non-Minkowski. The consequence would be that one would have to deal with quantum field theory in curved space which is much more complicated than QFT in a pure Minkowski-metric. I admit, I am not an expert on string theory (so the question might be seem basic for string theory experts) but I have some knowledge on General relativity, so I am rather curious how this issue is handled.

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