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These boundary conditions define a state of closed strings $|B\rangle$ and you can look at this paper or this one to learn more about this.

These boundary conditions define a state of closed strings $|B\rangle$ and you can look at this paper or this one to learn more about this.

If you write down a world-sheet with a closed string in a particular state that start from some location at the worldsheet and not at the infinity, the Diff plus Weyl gauge symmetries of the Polyakov action will be violated getting something that is gauge dependent. It means that this must be non physical since gauge symmetries are required to act trivially in physical states.

If you write down a world-sheet with a closed string in a generic state that start from some location at the worldsheet and not at the infinity, the Diff plus Weyl gauge symmetries of the Polyakov action will be violated getting something that is gauge dependent. It means that this must be non physical since gauge symmetries are required to act trivially in physical states.

In perturbative closed string theory, the amplitudes of are computed by summing over closed Riemann surfaces without boundaries. This is why we don't compute off-shell correlation functions like we do in QFT.

If you write down a world-sheet with a closed string in a particular state that start from a finite location and not at the infinity, the Diff plus Weyl gauge symmetries of the Polyakov action will be violated getting something that is gauge dependent. It means that this must be non physical since gauge symmetries are required to act trivially in physical states.

1. The first one is to push a boundary to infinity, where the Diff plus Weyl gauge is restored. There will be a conformal transformation that maps this "boundaries at infinity" (locations where the world-sheet becomes noncompact) to punctures at the world-sheet. This will define an asymptotic state.

In perturbative closed string theory, the amplitudes are computed by summing over closed Riemann surfaces without boundaries. This is why we don't compute off-shell correlation functions like we do in QFT.

If you write down a world-sheet with a closed string in a particular state that start from some location at the worldsheet and not at the infinity, the Diff plus Weyl gauge symmetries of the Polyakov action will be violated getting something that is gauge dependent. It means that this must be non physical since gauge symmetries are required to act trivially in physical states.

1. The first one is to push a boundary to infinity, where the Diff plus Weyl gauge invariance is restored. There will be a conformal transformation that maps this "boundaries at infinity" (locations where the world-sheet becomes noncompact) to punctures at the world-sheet. This will define an asymptotic state.