Unphysical sigma-models

However, postulating such form of action and BRST structure leads to some strange conclusion:

There are some sigma-models, which satisfy all these properties, and yet resist identification as a SUGRA background

These nonphysical states are of zero momentum, in this sense they are zero-modes. Morally speaking, they are close to what was called “discrete states” in bosonic string theory.

Unfortunately, it is not very straightforward to construct them. Conceptually, the simplest thing would be to construct them as excitations of . But in this talk, I do not want to go into AdS spaces.

I would rather prefer to obtain these states as perturbations of flat space. But unfortunately, flat space sigma-model is not of the type (1).

The generic action of the form (1) describes a generic curved background. Flat space turns out to be a singular limit.

I will now describe the sigma-model corresponding to flat space. It can be obtained as a limit of (1), but I will not explain how.