More on Membranes in Matrix Theory

TL;DR

This paper explores specific membrane solutions in Matrix theory, including a wormhole shape analogous to catenoids and holomorphic embeddings that preserve some supersymmetry, expanding understanding of membrane configurations.

Contribution

It introduces new static membrane solutions with axial symmetry and holomorphic embeddings in Matrix theory, highlighting their geometric and supersymmetric properties.

Findings

Derived a wormhole membrane solution with catenoid shape

Identified 1/4 BPS holomorphic membrane solutions

Connected membrane geometries to Born-Infeld theory shapes

Abstract

We study noncompact and static membrane solutions in Matrix theory. Demanding axial symmetry on a membrane embedded in three spatial dimensions, we obtain a wormhole solution whose shape is the same with the catenoidal solution of Born-Infeld theory. We also discuss another interesting class of solutions, membranes embedded holomorphically in four spatial dimensions, which are 1/4 BPS.