M5-branes, Special Lagrangian Submanifolds and sigma-models

TL;DR

This paper explores M-theory fivebranes wrapped on special Lagrangian submanifolds in Calabi-Yau spaces, revealing how their geometry influences resulting two-dimensional theories and connecting to recent mathematical constructions.

Contribution

It provides a physical realization of Hitchin's symplectic construction through M5-branes wrapped on specific cycles, linking geometry to sigma-model target spaces.

Findings

Two-dimensional domain walls with four supercharges are realized in M-theory.

Anomaly cancellation is achieved via gravitational Chern-Simons inflow.

Special Kähler manifolds emerge as sigma-model targets in specific brane configurations.

Abstract

We study M-theory fivebranes wrapped on Special Lagrangian submanifolds ($\S_n$) in Calabi-Yau three- and fourfolds. When the M5 wraps a four-cycle, the resulting theory is a two-dimensional domain wall embedded in three-dimensional bulk with four supercharges. The theory on the wall is specified in terms of the geometry of the CY manifold and the cycle $\S_4$. It is chiral and anomalous, however the presence of a three-dimensional gravitational Chern-Simons terms with a coefficient that jumps when crossing the wall allows to cancel the anomaly by inflow. Kahler manifolds of special type, where the potential depends only on the real part of the complex coordinate, are shown to emerge as the target spaces of two-dimensional sigma-models when the M5 is wrapped on $\S_3 \times S^1$, thus providing a physical realization of some recent symplectic construction by Hitchin.