Quantum Mathematical Physics Seminar

The Kontsevich-Witten model provides a cornerstone of mathematical physics, linking topological gravity, intersection theory on the moduli space of stable curves, and matrix model representations of Virasoro constraints. In this talk, we present a unified supercurrent formulation of $\mathcal{N}=1$ super-Virasoro constraints aimed at an external source description for supersymmetric extensions of the Kontsevich model. We introduce a super-Miwa transformation that translates infinite hierarchy times into finite spectral variables, representing projected super energy-momentum tensors as explicit differential operators. We show that cubic dilaton shifts yield standard Super Quantum Airy Structures in the NS--NS and R--NS sectors, whereas the R--R and NS--R sectors require an auxiliary odd coordinate or central constraint to resolve Ramond zero modes. Our central result is an exact similarity transformation in spectral variables that intertwines the NS--NS and R--R differential constraints.