Determine whether the Airy-function structure breaks down for the twisted affine A^{(2)}_{2r} quiver

Determine whether the large-N expansion of the affine A^{(2)}_{2r} quiver matrix model with balanced ranks and Fresnel measures retains or breaks down the Airy-function structure.

Background

The paper studies Fermi-gas descriptions of matrix models associated with affine BC and twisted affine AD quivers. For the B^{(1)}_r, C^{(1)}_r, A^{(2)}_{2r-1}, and D^{(2)}_{r+1} models, the authors identify a logarithmic term in the classical Hamiltonian that produces an E log E correction to the semiclassical density of states and prevents the usual Airy-function form of the perturbative 1/N expansion.

For the A^{(2)}_{2r} model, the factors involving the momentum operator cancel in the density matrix, so its classical Fermi surface is indistinguishable from that of an affine A-type quiver. The authors therefore cannot determine from their analysis whether the Airy-function structure survives or fails in this case, leaving this as an unresolved problem.