In: Physics
Imagine, if you will, a string background with an extremely tiny value for the string coupling. The Planck scale is many orders of magnitude smaller in size than the string scale. Is the UV/IR mixing scale the Planck scale, or the string scale? What happens at intermediate scales?
Gravitons are string modes, and as such, their spatial extent is the string scale. They can never resolve anything smaller than that. On the other hand, D-branes are more sensitive
In perturbative string theory, for , it's always
the string scale where the UV/IR mixing happens first. It's the
lightest mass scale associated with the lightest (possibly
extended) objects - and in perturbative string theory regimes, it's
always the fundamental strings. For example, the low-energy
spectrum at masses below
is
always related to the high-energy spectrum at masses above
by
the modular invariance (of the toroidal world sheet) - and
similarly for open strings and cylindrical world sheets.
Different effects may see different forms of UV/IR mixing for
which different scales are relevant, however. The term UV/IR mixing
is a somewhat vague, umbrella term that covers many effects in
string theory or quantum gravity. D-branes may resolve shorter
distances than the string scales but there is actually always some
sense in which even e.g. D0-branes are linked to the string scale.
If they resolve distances and times
, then
. Yoneya would play with insights like this. D0-branes may resolve
sub-stringy distances but only if their velocity is very small, in
which case they can only measure the time with
much-worse-than-stringy resolution.
There are also - less understood - aspects of the UV/IR mixing that arise at the Planck scale. But some of them are known so incompletely that the arguments are only valid up to the assumption that g is considered to be of order one. The relevant scale where geometry - with degrees of freedom at each "layer" of scales being independent of each other - fails to be applicable is always given by the scale associated with the first higher-order corrections to the Einstein-Hilbert action etc. and it's always the string scale i.e. the scale associated with the tension of the lightest fundamental objects