General relativity from string theory

[atyy]

Some of the classical no-go theorems that Haelfix mentions are referenced in http://arxiv.org/abs/hep-th/0106109v1 , one of which is http://arxiv.org/abs/hep-th/0007018 .

 

[Finbar]

oh come on ricci flatness is hardly deep if you didn't have it then you'd violate energy conservation.

 

[nrqed]

Hi Nrqed, that is a truly excellent question and way above the level of Tong.

(for the identical statement said slightly differently, see Polchinksi):
http://books.google.com/books?id=k4...age&q=coherent states vertex operator&f=false

I think the answer to your first question is almost but not quite. The problem is there are gauge fixing ambiguities creeping into the calculation, and you have to ensure the symmetries of string theory (Virasoro constraints) are enforced. Consequently the naive definition of a coherent state must be slightly generalized to ensure this.

But once that is done, then yes there is a sense in which you can show that what you get is an eigenstate of the annihilation operator, although the paper I am looking at is technically challenging...

See
http://arxiv.org/abs/0911.5354v2 starting on page 27 for a discussion and the calculation for eg closed strings in lightcone gauge is on page 36, although the vertex operators are more general (DDF vertex operators). Maybe one of the stringy experts here knows a simpler calculation, but I have never seen it done nor could I find it in a quick literature search. I am actually a little surprised that I couldn't find the calculation done in texts regarding nonminimal sigma models, since this is very much isomorphic.

Thank you Haelfix, I truly appreciate your explanations. I will look at the references with great interest.