  We predict the generation of noncritically squeezed light through the
spontaneous rotational symmetry breaking occurring in a Kerr cavity. The model
considers a $\chi^{(3)}$ cavity that is pumped by two Gaussian beams of
frequencies $\omega_{1}$ and $\omega_{2}$. The cavity configuration is such
that two signal modes of equal frequency $\omega_{\mathrm{s}}=(\omega_{1}%
+\omega_{2})/2$ are generated, these signal fields being first order
Laguerre--Gauss modes. In this system a spontaneous breaking of the rotational
symmetry occurs as the signal field corresponds to a Hermite--Gauss TEM mode.
This symmetry breaking leads to the perfect and non--critical (i.e., non
dependent on the parameter values) squeezing of the angular momentum of the
output TEM mode, which is another TEM mode spatially orthogonal to that in
which bright emission occurs.
