Discussion:
Very Basic Question
(too old to reply)
s***@yahoo.com
2005-06-06 15:16:22 UTC
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I'm doing some background reading for
http://arxiv.org/abs/hep-th/0505188

and there is something very basic that
I'm getting badly confused about. We all know
that in string theory there are higher-order
corrections to the Einstein-Hilbert lagrangian
coming both from loops and from alpha' corrections.
Let's think about the alpha' corrections. Normally
people say that these higher-order curvature terms
are "suppressed" by powers of alpha'. My question
is this: in four dimensions, the coefficients would
really be things like alpha'/G, where G is Newton's constant.
This is [L_s/L_p]^2 , where L_s is the string length
scale and L_p is the Planck length. But normally,
if we believe in weakly coupled strings, this is a
*large* number, not a small one! So in what sense
are the string corrections to the EH lagrangian
"suppressed"? I know this has some very simple
answer, somebody please kick me........
Lubos Motl
2005-06-06 15:23:48 UTC
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My question is this: in four dimensions, the coefficients would really
be things like alpha'/G, where G is Newton's constant.
Dear Serenus,

I don't think that this is a question. I would rather call it an incorrect
statement. The first leading alpha' corrections look like

alpha' R^2 / G

Relatively to the Einstein-Hilbert action "R / G", they're suppressed by

alpha' . curvature

which is dimensionless and very small if the curvature radius is much
longer than the string scale. I suppose that you added "1/G" to alpha' in
order to make the expansion parameter dimensionless, but it was just your
(incorrect) choice, not a necessity and not a consequence of string
theory. String theory gives you "alpha'.curvature" as one expansion
parameter and "g_{string}" as a second expansion parameter and both of
them are small in weakly coupled string theory on large manifolds.

The alpha' R^2 corrections in 10 or 11 dimensions lead to similar
corrections in four; alpha' R^2 in four dimensions is among them.

All the best
Lubos
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