We write down a local ${\mathrm{CP}}_1$ model involving two gauge fields, which is exactly equivalent to the O(3) σ model with the Hopf term. We impose the ${\mathrm{CP}}_1$ constraint by using the Gaussian representation of the delta function. For the coefficient of the Hopf term, θ= π / 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 σ model.

• Received 4 March 1992

DOI:https://doi.org/10.1103/PhysRevLett.69.721