The “Null-A” superintegrability for monomial matrix models

Abstract

We find that superintegrability (character expansion) property persists in the exotic sector of the monomial non-Gaussian matrix model, with potential TrXr, in pure phase, where the naive partition function 〈1〉 vanishes. The role of the (anomaly-corrected) partition function is played by χρ – the Schur average of the suitably chosen rectangular partition ρ; such partitions are well-known to correspond to singular vectors of the Virasoro algebra. Further, non-zero are only Schur averages χμ for such μ that have ρ as their r-core, and superintegrability formula features the value of the skew Schur function χμ/ρ at special point. The associated topological recursion and Harer–Zagier formula generalizations so far remain obscure.