group $G$.
The charge $Q$ \potfour\ of $G$-models is
$$
Q=\int dx \big(\kappa_A (L-R)^A_i\partial_t\phi^i+\kappa_A  
(L+R)^A_i\partial_x\phi^i +\partial_x a \big)\ .
\eqn\fourbb
$$
For $G$ abelian, $L=R$ and $\_A(L+R)\^A$ is a closed one-form, so
$Q\_N=0$ and
$$
Q_T=Q=\int \, dx\, \big(2\kappa_A L^A_i\partial_x\phi^i +\partial_x a \big)\ .
\eqn\potninea
$$  
However, for $G$ semisimple, the one-form $u-da$ is  co-exact and the
topological charge $Q\_T$ \potsix\  is
simply
$$
Q_T=\int dx \partial_x a\ .
\eqn\potnine
$$

To find the mass and charge of the bosonic fundamental  states of
$G$-models, we use the background field method (see for example
[\hps]) to linearise the theory around a
classical supersymmetric vacuum $k\_0$. The mass-square and charge    
matrices written in the left-invariant
frame basis are then
$$
{\cal M}_{AB}={m^2\over4}\big(\kappa^C \kappa^D f^E{}_{AC}\, f_{EBD}+
n^2 \sum_C{\rm tr}\,(t_{(A}\, t_{C)}
k_0^n)\,{\rm tr}(t_{(B}\, t_{C)} k_0^n)\big)\ ,
\eqn\potten
$$
and
$$
{\cal Q}_{AB}=-\kappa^C f_{ABC}\ ,
\eqn\poteleven
$$
respectively. The eigenvalues of  $[M]{}$ are the  square of the 
masses of the fundamental
states and the eigenvalues of $[Q]{}$ are their charges.  To do
this computation, we have used
\pottwo\ to show that
$du=0$ evaluated at any supersymmetric vacuum.  The fundamental states
parallel to the zero modes of the charge-matrix
\poteleven\ have zero Noether charge. The zero 