If |ψ⟩ is a string mode, how do you compute ⟨ψ|ˆTμν(→x)|ψ⟩ where →x is a point in target space? This information will tell us the energy distribution of a string. In string theory, the size of a string grows logarithmically as the worldsheet regulator scale. In the limit of zero regulator size, all strings are infinite in size, and this ought to show up in the stress-energy distribution.
What about multi-string configurations? The vacuum has virtual string pairs. Only the spatial average ∫d9xˆT00(→x)|0⟩=0. ˆT00(0)|0⟩≠0 even though ⟨0|ˆT00(0)|0⟩=0. Here, |0⟩ is the string vacuum. The stress-energy operator can create a pair of strings. It doesn't preserve the total number of strings.
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