Arithmetic Decompactification at Asymmetric WZW Endpoints

We analyze critical limits of the exactly marginal asymmetric deformation of the supersymmetric \(SU(2)_k\) Wess--Zumino--Witten model, distinguishing charge-spectrum, dual, and fixed-identification geometric limits. The affected \(O(1,1)\) lattice reaches its critical field at infinite current--current Zamolodchikov distance \(t=2|x|\). For \(k_G=2\) and \(k=2p^2\), we classify the stable integral charge kernel as a finite union of affine lattices. Its primitive branch has \(\Delta_\ell-\Delta_{\rm core}=4p^2\ell^2 e^{-t}\); a uniform gap separates complementary charges. Poisson summation yields one noncompact Gaussian spectral direction with a controlled remainder and counting discrepancy. After right chiral duality, the stable limit is a connected noncompact line, whereas the original Berger-sphere metrics collapse to \(S^2\). For completions satisfying the specified operator-level duality and GSO conditions, including the analyzed diagonal heterotic fivebrane throats, we identify the BRST complexes and the free-line transfer kernel. We give explicit endpoint stability tests and distinguish rational from irrational stable slopes. The endpoint geometry and BRST conclusions depend on the stated completion and polarization; they are not a proof that the fixed target-space topology changes.