# 11D and enhanced gauged symmetry when alpha=R2

1. Nov 9, 2009

### arivero

First of all, who discovered the enhancement of symmetry in compactified theories, when the radius of the compact dimension equals the square root of the string tension? Polchinski gives an expanded example, and GSW already mentions the effect, but without references in any of the books.

It is strange that, being Witten already interested on D=11 when GSW was written, there is no mention about the possibility of relating this enhancement to the grown of an extra dimension for some limits. Duality goes by $R_A= L_p^2/R_B$, with [itex]L_p[/tex] the string scale (1 GeV in dual models, 10^19 someV in divulgative terms, anyeV in Randallized models). One could consider to research the limits where the string scale goes to zero or to infinity. Also, the proportionality between the compactified radius and the string scale sets the coupling constant of the KK gauge theory and it could be interesting to consider both limits.

Now, given that the enhancement, for nonoriented strings, is from U(1) to SU(2), and given that U(1) can be realised in 1d space while SU(2) needs a 2d compact space, is it possible to claim that an extra dimension happens in this case? Has someone claimed it explicitly, somewhere, right or wrong?