Gauge fields on the stability subgroup of the vacuum in a nonlinear realization

In models with nonlinear realization of symmetry, one can introduce gauge fields without localization of group transformations. Such fields may arise under definite conditions on stability subgroups of the vacuum. In this paper, we propose a method of construction of the corresponding effective Lagrangian. For the example of $SU(2)\times SU(2)$ symmetry, it is shown that the proposed construction is compatible with the ordinary gauge models that arise as a result of direct breaking of the gauge symmetry from Lagrangians constructed in accordance with the inverse Higgs effect.