Global Symmetries
N.B. : Here, a symmetry is said to be local or global from the two dimensional theory (on the worldsheet) point of view. For example, Lorentz transformations, that are local symmetries of the space-time, are global symmetries of the theory on the worldsheet.
The action is invariant under spacetime translations and infinitesimal Lorentz transformations:
- (i)
- (ii)
where and is a constant. This forms the Poincaré symmetry of the target manifold.
The invariance under (i) follows since the action depends only on the first derivative of . The proof of the invariance under (ii) is as follows:
Read more about this topic: Polyakov Action
Famous quotes containing the word global:
“Ours is a brand—new world of allatonceness. “Time” has ceased, “space” has vanished. We now live in a global village ... a simultaneous happening.”
—Marshall McLuhan (1911–1980)