U-duality from Matrix Membrane Partition Function

TL;DR

This paper demonstrates how the partition function of a supersymmetric matrix model captures U-duality invariance in supermembrane instanton sums, highlighting the significance of supermembrane interactions.

Contribution

It shows that the supermembrane partition function, when mapped to a cohomological theory and mass-deformed, reproduces the U-duality invariant measure, unlike previous zero-mode analyses.

Findings

Partition function matches U-duality invariant measure

Mass deformation is crucial for invariance

Self-interactions are essential for correct results

Abstract

We analyse supermembrane instantons (fully wrapped supermembranes) by computing the partition function of the three-dimensional supersymmetrical U(N) matrix model under periodic boundary conditions. By mapping the model to a cohomological field theory and considering a mass-deformation of the model, we show that the partition function exactly leads to the U-duality invariant measure factor entering supermembrane instanton sums. On the other hand, a computation based on the quasi-classical assumption gives the non U-duality invariant result of the zero-mode analysis by Pioline et al. This is suggestive of the importance of supermembrane self-interactions and shows a crucial difference from the matrix string case.