The Super-Toda System and Bubbling of Spinors

Abstract

We introduce the super-Toda system on Riemann surfaces and study the blow-up analysis for a sequence of solutions to the super-Toda system on a closed Riemann surface with uniformly bounded energy. In particular, we show the energy identities for the spinor parts of a blow-up sequence of solutions for which there are possibly four types of bubbling solutions, namely, finite energy solutions of the super-Liouville equation or the super-Toda system defined on ${\mathbb{R}}^2$ or on ${\mathbb{R}}^2\setminus \{0\}$. This is achieved by showing some new energy gap results for the spinor parts of these four types of bubbling solutions.