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arXiv · 2608.12247

Quantum Airy Structures and Matrix Models: a supercurrent approach

Leszek Hadasz·Mykhailo Hontarenko
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Abstract

We develop a super-current formulation of $\mathcal{N}=1$ super-Virasoro constraints for external-source models. By assigning bosonic and fermionic monodromies independently, we unify the NS-NS, NS-R, R-NS, and R-R sectors. For each, a super-Miwa transformation represents the projected super energy-momentum tensor as a differential operator in spectral variables. Dilaton shifts yield Super Quantum Airy Structures in the NS-NS and R-NS sectors, whereas the R-R and NS-R sectors require an additional odd coordinate. Our principal result is an exact similarity transformation relating the NS-NS and R-R differential constraints. The intertwining prefactor combines a bosonic determinant, a cubic Airy weight, and a Grassmann exponential kernel defined by the difference of Neveu--Schwarz and Ramond fermionic propagators. These results establish a concrete candidate system of Ward identities for a supersymmetric extension of the Kontsevich model, delineating the precise algebraic and analytic properties of the measure and fermionic kernel required for its potential matrix-model realization.

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Leszek Hadasz, Mykhailo Hontarenko. 2026-08-12. Quantum Airy Structures and Matrix Models: a supercurrent approach. https://arxiv.org/abs/2608.12247

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