I\'m taking a course in string theory and have encountered renormalization for t

Question

I'm taking a course in string theory and have encountered renormalization for the first time (and I suspect it isn't the last).

Specifically, while quantizing the bosonic and spinning strings, an ordering ambiguity in the mode expansion gives us a constant (called 'a' in the notes I'm reading) which is a divergent sum. The constant is then fixed to 1 (at least for the bosonic string in light-cone quantization - don't remember the others at the moment) by some very convincing physical arguments reminiscent of renormalization in good ol' QFT.

My question is: why would we expect something like this to be necessary? Isn't the whole philosophy of renormalization that the necessity for adjustment of parameters comes out of the fact that your QFT is an effective low-energy approximation of some complete theory? If this complete theory is a string theory, then why do we still encounter the need for renormalization?

Explanation / Answer

There are two separate issues here:

Worldsheet versus Spacetime:

String theory is a generalization of quantum field theory, but perturbative string theory is formulated in a language pre-dating QFT. In Schwinger

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