How exactly does non-critical string theory avoid conformal anomaly?

Question

I will soon be introducing myself to non-critical string theory, and I think it could be nice to have a little primer on it.

What I understand so far out of non-critical string theory is that conformal anomaly (which can be expressed in terms of ghost states, or breaking of Lorentz invariance, etc. as in critical string theory) is still zero, but this is done without any constraints on the critical dimension.

But how exactly is this done? Surely, something else must be constrained if the critical dimension is free to be chosen? What happens to the normal ordering constant? Is it also free to be chosen, or is it constrained in some way? If nothing new is constrained, what are the changes made to the theory to avoid conformal anomaly?

Answer 1

There's an extra field with an exponential potential ("Liouville field", as Polyakov named it--- better name is "Polyakov field"). It's covered in Polyakov.

Comments

Hi Ron, could you give the reference of link to the Polyakov, I dont know what paper (?) you exactly mean ...?

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@Dilaton I think he means Polyakov's string theory textbook.