# Coupling fermions to a scalar field: Interpretation problem

1. ### blue2script

49
Hi all,

I have a little problem concerning the coupling of a fermion to CP^N (or better a 2D scalar O(3) model). Its not a mathematical type of problem. I just read on

"The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions"

http://arxiv.org/PS_cache/hep-th/pdf/0402/0402013v2.pdf

The Lagrangian of this theory is written down in (2.1) and I am a bit lost as of interpreting this formula. There are three indegredients: 1. a scalar field, 2. a fermionic field and 3. a gauge field. Now, a scalar field represents a spin-0 field, right? The fermionic field is of spin 1/2. But now what is the gauge field? The scalar field may have some internal symmetry like O(3) but this won't affect the Lagrangian. I just don't understand what the gauge field is in this case.

Could somebody explain that to me? A big thanks in advance!!

Blue2script

PS: Also, of what physical interest is the scalar model besides being a nice toy model to study field effects? What could be the interpretation of a scalar field?

2. ### masudr

932
For example, in a chiral supermultiplet, you can have a scalar field and Weyl fermion fields in the same supermultiplet.

Such scalar fields are candidates for the inflaton field that led to inflation (the Higgs doesn't quite work as that field).