Knots, Braids and BPS States in M-Theory

TL;DR

This paper extends previous M-theory five-brane analyses by using knot and braid theory to compute light BPS states near singularities in elliptic Calabi-Yau threefolds, revealing new insights into the spectrum of such states.

Contribution

It introduces a novel method of using knots and braids to analyze singularities in M-theory compactifications, enabling the computation of BPS spectra near complex singular loci.

Findings

Successfully computed BPS states near singular points with N=2 supersymmetry.

Demonstrated the effectiveness of knot and braid techniques in string theory contexts.

Extended the understanding of five-brane dynamics on singular Calabi-Yau spaces.

Abstract

In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near the smooth part of the discriminant curve. In this paper, we extend that work to compute the light states on the worldvolume of five-branes wrapped on fibers near certain singular loci of the discriminant. We regulate the singular behavior near these loci by deforming the discriminant curve and expressing the singularity in terms of knots and their associated braids. There braids allow us to compute the appropriate string junction lattice for the singularity and,hence to determine the spectrum of light BPS states. We find that these techniques are valid near singular points with N=2 supersymmetry.