duality was the major discovery during the period between string
revolutions from 1986-1992. The simplest case has one compact dimension
a circle of radius R.
Momentum excitations: En
Winding mode excitations: Em
= 2 p T R m
T is the string tension T = (2 p
T duality is the invariance of a theory
under switching m with n
and R with Lst2/R.
The implication of T duality is that
quantum geometry at short distances falls under a new Generalized Uncertainty