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

Abstract

We write down a local $C{P}_1$ model involving two gauge fields, which is exactly equivalent to the O(3) $\sigma$ model with the Hopf term. We impose the $C{P}_1$ constraint by using the gaussian representation of the delta function. For the coefficient of the Hopf term, $\theta =\frac{\pi }{2s}$, 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.

11 pages

Cited by in corpus (4)

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