Nonperturbative structure of lower-degree discrete-volume components

Determine the nonperturbative structure of the lower-degree components of the discrete volumes N_{g,n} governing ETH matrix-model amplitudes, in order to obtain subleading-in-λ corrections beyond those captured by the q-deformed Weil–Petersson volumes V^q_{g,n}.

Background

The leading nonperturbative correction is protected because only the top-degree part of the discrete volume contributes at leading order in the small-λ expansion; this top-degree part is represented by the q-deformed Weil–Petersson volume.

Subleading corrections require the nonperturbative behavior of the lower-degree remainder of N_{g,n}, which the paper does not determine in general. This unresolved input prevents the authors from extending their general method to subleading powers of λ.