The low lying spectrum of the 2d grassmannian non-linear models

We present analytic results for the mass gap values, of the two-dimensional grassmannian models $\text{SO}\text{(p + q)}\text{SO}\text{(p)}\text{×}\text{SO}\text{(q),}\text{SU}\text{(p + q)}\text{SU}\text{(p)}\text{×}\text{SU}\text{(q) ×}\text{U}\text{(1)}\text{and}\text{Sp}\text{(p + q)}\text{Sp}\text{(p) ×}\text{Sp}\text{(q)}$. The finite volume effective hamiltonian of these models is constructed to one-loop order.