The careful reader has patiently suspended disbelief for a while now, allowing us to race through a somewhat rough presentation of some of the highlights of the construction of consistent relativistic strings. This enabled us, by essentially stringing lots of oscillators together, to go quite far in developing our intuition for how things work, and for key aspects of the language.

Without promising to suddenly become rigourous, it seems a good idea to revisit some of the things we went over quickly, in order to unpack some more details of the operation of the theory. This will allow us to develop more tools and language for later use, and to see a bit further into the structure of the theory.

Conformal invariance

We saw in section 2.2.8 that the use of the symmetries of the action to fix a gauge left over an infinite dimensional group of transformations which we could still perform and remain in that gauge. These are conformal transformations, and the world-sheet theory is in fact conformally invariant. It is worth digressing a little and discussing conformal invariance in arbitrary dimensions first, before specialising to the case of two dimensions. We will find a surprising reason to come back to conformal invariance in higher dimensions much later, so there is a point to this.