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There is obviously a gap in my knowledge of the origin of effective actions in string theory.

As far as I understand it, the strategy is straightforward (at least in principle):

  1. Write down the worldsheet action for the superstring.
  2. Take compactification and (or) localization into account, obtain a low-energy action for the brane.
  3. Re-interpret this action as a QFT on the brane with a natural cut-off of order $l_s$ (string length).

OK, so that explains why we have a field-theoretic action of some form. However there is no reason (besides our intuition) for it to generate a QFT.

In path integral formulation, the fundamental measure comes from the (supersymmetric version of) Polyakov path integral over the fields on the superstring worldsheet.

It seems to me that it could (in general) generate another low-energy "effective measure", spanning another QFT.

How does one show that this is not the case?

Prof. Legolasov
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1 Answers1

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In general, once you fix the high energy theory, then there will be a unique EFT following from running down that theory to some lower energy $E_L$ (which will depend of course on $E_L$). Note however that deriving this EFT can be highly complicated sometimes. If for any reason the EFT you get at $E_L$ is not what you wanted, then you have to modify the high energy theory and start again. There is no other option.

The EFT you get might be quantum or not, sometimes depending on how far down you go. For example, you can take QFT down to QM or even all the way down to Newtonian physics (at least in principle). Mathematically, you can see if the resulting theory is quantum or not by looking at the commutators of the operators in the EFT and checking if they are small enough to be ignored or not.

Heterotic
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