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I'm going to stick my neck out here and summarize the comment threads above as an answer of sorts. I'll delete it if it pulls down my reputation score :-/ The universe in which we happen to find ourselves is, as near as we can tell, not structured in a way that would support different values of its fundamental parameters in different locations within it- ...


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From Polchinski's String Theory, Chapter 1: We want to study the classical and quantum dynamics of a one-dimensional object, a string. The string moves in $D$ flat spacetime dimensions, with metric $\eta_{\mu \nu} = \mathrm{diag}(-,+,+,\cdots,+)$. So all additional dimensions are spacelike. Strictly speaking Polchinski is only talking about bosonic ...


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FWIW, eq. (2.1.14) is in the Euclidean formulation, while eq. (A.1.17) is in the Minkowskian formulation. The operators inside the expectation value on the LHS of eq. (2.1.14) are implicitly assumed to be radially ordered.


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