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 $\Tr X^r$, in pure phase, where the naive partition function $⟨1⟩$ vanishes. The role of the (anomaly-corrected) partition function is played by $⟨{\chi }_{\rho }⟩$ -- the Schur average of the suitably chosen \textit{square} partiton $\rho$; such partitions are well-known to correspond to singular vectors of the Virasoro algebra. Further, non-zero are only Schur averages $⟨{\chi }_{\mu }⟩$ for such $\mu$ that have $\rho$ as their $r$-core, and superintegrability formula features the value of the \textit{skew} Schur function ${\chi }_{\mu /\rho }$ at special point. The associated topological recursion and Harer-Zagier formula generalizations so far remain obscure.

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Cited by in corpus (2)

• On bilinear superintegrability for monomial matrix models in pure phase
• Towards mixed phase correlators in monomial matrix models