The Super-Toda System and Bubbling of Spinors

TL;DR

This paper studies the super-Toda system on Riemann surfaces, analyzing blow-up behavior of solutions, and establishes energy identities and gap results for spinor components during bubbling phenomena.

Contribution

It introduces the super-Toda system on Riemann surfaces and provides new energy gap results and identities for spinor parts during blow-up analysis.

Findings

Identified four types of bubbling solutions for the super-Toda system.

Established energy identities for spinor components in blow-up sequences.

Proved new energy gap results for spinor parts of bubbling solutions.

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 $\R^2$ or on $\R^2\setminus\{0\}$. This is achieved by showing some new energy gap results for the spinor parts of these four types of bubbling solutions.