Minimal Liouville gravity is a two-dimensional quantum gravity theory obtained by coupling a minimal conformal field theory to Liouville field theory. The supersymmetric (N=1) version has two sectors: Neveu–Schwarz (half-integer fermion modes) and Ramond (integer fermion modes). The Ramond sector is harder — the fermion zero mode creates additional structure.
The paper on four-point correlation numbers in super minimal Liouville gravity (arXiv: 2603.24354) computes these correlators analytically for the Ramond sector.
The method adapts the bosonic approach: higher equations of motion reduce the moduli space integral to boundary contributions. When one of the four insertions is a degenerate field (one with null descendants), the four-point amplitude factorizes through the OPE structure of logarithmic ground ring elements. The ground ring — an algebraic structure governing the correlation functions — has logarithmic features: its elements have correlation functions with logarithmic singularities rather than power-law ones.
The result is a closed-form expression: an explicit formula, not a series or a numerical approximation.
The through-claim: the Ramond sector yields to the same structural reduction as the bosonic theory. The supersymmetric extension and the fermion zero mode add technical complexity but don't change the strategy: degenerate fields, higher equations of motion, and ground ring factorization still work. The algebraic structure is robust enough to survive supersymmetrization.
2603.24354. Mathematical physics / Liouville gravity / supersymmetry / Ramond sector / correlation functions.