A non-linear sigma model, whose action is generically given by $$S_\text{NLSM}=\int d^dx\, g_{ij}\partial_\mu\phi^i\partial^\mu\phi^j$$ has a natural geometric interpretation that $\phi$ is a map $\mathcal{M}\to\mathcal{T}$, where $\mathcal{M}$ is the ambient spacetime and $\mathcal{T}$ is a "target space". Then one can think of $g_{ij}$ as a metric on the target space $\mathcal{T}$.
However, suppose we have a Landau-Ginzburg model with action $$S_\text{LG}=\int d^dx\, \left(g_{ij}\partial_\mu\phi^i\partial^\mu\phi^j-V(\phi)\right).$$ Can $\phi$ still be interpreted as a map $\mathcal{M}\to\mathcal{T}$ with $g_{ij}$ being a metric on $\mathcal{T}$? If not, then is there still a geometric interpretation of some sort?
