- #1

blue2script

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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?