But Background Spacetime *Is* Gravity In String Theory.

Experts can correct me if I'm wrong, but I believe the below is correct.

As said before, loop quantum gravity supporters, and many quantum gravity people in general, argue a major problem with string theory is that it isn't background dependent.  Physically, they argue, this is bad since from GR we learn gravity doesn't propagate through spacetime but in fact is the spacetime.

However, I believe this critique may be unfounded.   It turns out, curved spacetime in string theory is a cohert state of gravitons, not just some ad hoc background space for strings to move through. (As our LQG friends world have us believe.)

Here's how to see it. Again from David Tong's wonderful lecture notes:

The string action in curved space:  (Capital G is the "background space").

The trick is to put G into the form: (We do this all the time.  Nothing fishy here.)

Now, throw that puppy into the path integral, and we have:

Where S_Poly is string theory without curved space and V is:

But V is just the vertex operator for a graviton!

For those who don't know, inserting a single vertex operator V in the path integral corresponds to the introduction of a single graviton state. Inserting e^(V) in the path integral corresponds to a coherent state of gravitons!

So, the background in string theory does not appear to be some ad hoc background the strings are magically propagating in.  It appears to be a coherent state of the gravitons themselves.

Hence, I believe the critics are wrong: Curved spacetime in string theory appears to be nothing more than gravitons after all.  Just like GR.