  We consider the Chalker-Coddington network model for the Integer Quantum Hall
Effect, and examine the possibility of solving it exactly. In the
supersymmetric path integral framework, we introduce a truncation procedure,
leading to a series of well-defined two-dimensional loop models, with two loop
flavours. In the phase diagram of the first-order truncated model, we identify
four integrable branches related to the dilute Birman-Wenzl-Murakami
braid-monoid algebra, and parameterised by the loop fugacity $n$. In the
continuum limit, two of these branches (1,2) are described by a pair of
decoupled copies of a Coulomb-Gas theory, whereas the other two branches (3,4)
couple the two loop flavours, and relate to an $SU(2)_r \times SU(2)_r /
SU(2)_{2r}$ Wess-Zumino-Witten (WZW) coset model for the particular values $n=
-2\cos[\pi/(r+2)]$ where $r$ is a positive integer. The truncated
Chalker-Coddington model is the $n=0$ point of branch 4. By numerical
diagonalisation, we find that its universality class is neither an analytic
continuation of the WZW coset, nor the universality class of the original
Chalker-Coddington model. It constitutes rather an integrable, critical
approximation to the latter.
