M2-brane matrix models and Fermi gas on affine ABCD quivers

Abstract: We study a new class of M2-brane matrix models associated with affine BC and twisted affine AD quivers. These models exhibit the characteristic $N<sup>{3/2}$ scaling of the free energy in the large $N$ limit. We establish a Fermi gas formalism and demonstrate that their grand canonical sum is given by a Fredholm Pfaffian, which is in parallel with the affine D quiver matrix models. The resulting Fermi gas density matrix shows a rational dependence on the canonical position/momentum operators in addition to the standard hyperbolic dependence. This leads to unconventional sub-leading corrections, which obstruct the Airy function structure in the $1/N$ expansion of the free energy observed in the previously studied M2-brane matrix models.