BPS States and Minimal Surfaces

TL;DR

This paper links BPS states in supersymmetric theories to minimal surfaces in M Theory, demonstrating how membrane topology determines supermultiplet types and connecting to string theory compactifications.

Contribution

It proves the BPS spectrum for SU(2) Super Yang-Mills from minimal surface configurations and develops methods for analyzing BPS states in broader contexts.

Findings

BPS states correspond to minimal area membranes ending on fivebranes.

Membrane topology determines supermultiplet type: disks for hypermultiplets, cylinders for vector multiplets.

The approach relates minimal surfaces to string compactification geometries.

Abstract

It was observed recently, that the low energy effective action of the four-dimensional supersymmetric theories may be obtained as a certain limit of M Theory. From this point of view, the BPS states correspond to the minimal area membranes ending on the M Theory fivebrane. We prove that for the configuration, corresponding to the SU(2) Super Yang-Mills theory, the BPS spectrum is correctly reproduced, and develop techniques for analyzing the BPS spectrum in more general cases. We show that the type of the supermultiplet is related to the topology of the membrane: disks correspond to hypermultiplets, and cylinders to vector multiplets. We explain the relation between minimal surfaces and geodesic lines, which shows that our description of BPS states is closely related to one arising in Type II string compactification on Calabi-Yau threefolds.