Monday, March 8, 2010

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.


  1. My question is whether a background of coherent states of gravitons is any improvement. Your background does have something to do with a string model of gravity, but you still have a particular background in which stuff happens. The point I take away from GR is that stuff doesn't just happen, but stuff-spacetime configurations occur (simply put).

  2. Ben, maybe it is not an improvement. I don't know enough to say for sure.

    But it at least makes me happy knowing the background isn't completely ad hoc but actually is just the gravitons, like GR.

  3. I give Radhasoami Faith view of Creation Theory. In Sar Bachan (Poetry) composed by His Holiness Soamiji Maharaj the August Founder of Radhasoami Faith the details of creation and dissolution has been described very scientifically. It is written in this Holy Book: Only He Himself (Supreme Father)and none else was there. There issued forth a great current of spirituality, love and grace (In scientific terminology we may call this current as gravitational wave). This is called His Mauj (Divine Ordainment). This was the first manifestation of Supreme Being. This Divine Ordainment brought into being three regions, viz., Agam, Alakh, and Satnam of eternal bliss. Then a current emerged with a powerful sound. (first big bang) It brought forth the creation of seven Surats or currents of various shades and colours (in scientific terminology we may call it electromagnetic waves). Here the true Jaman or coagulant was given (in scientific terminology this coagulant may be called as weak nuclear force and strong nuclear force). Surats, among themselves, brought the creation into being.
    These currents descended down further and brought the whole universe/multi verse into being i.e. black holes, galaxies etc. were born.


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