Is the $O(3)~σ$ Model with the Hopf Term Exactly Equivalent to a Higher Spin Theory?

Details Is the $O(3)~σ$ Model with the Hopf Term Exactly Equivalent to a Higher Spin Theory? Is the $O(3)~σ$ Model with the Hopf Term Exactly Equivalent to a Higher Spin Theory?

1992-03-02

arxiv.org/abs/hep-th/9203013v1

Phys.Rev.Lett. 69 (1992) 721-724

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1103/PhysRevLett.69.721

We write down a local $CP_1$ model involving two gauge fields, which is exactly equivalent to the O(3) $\sigma$ model with the Hopf term. We impose the $CP_1$ constraint by using the gaussian representation of the delta function. For the coefficient of the Hopf term, $\theta = {\pi \over 2s}$, 2s being an integer, we show that the resulting model is exactly equivalent to an interacting theory of spin-$s$ fields. Thus we conjecture that there should be a fixed point in the spin-$s$ theory near which it is exactly equal to the $\sigma$ model.

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