RG domain wall for the general s u ^ 2 $$ widehat{su}(2) $$ coset models

We consider a rg flow in a general $$ widehat{su}(2) $$ coset model induced by the least relevant field. this is done using two different approaches. we first compute the mixing coefficients of certain fields in the uv and ir theories using a conformal perturbation theory. the necessary structure constants are computed. the same coefficients can be calculated using the rg domain wall construction of gaiotto. we compute the corresponding one-point functions and show that the two approaches give the same result in the leading order.