Bloch Waves and Fuzzy Cylinders: 1/4-BPS Solutions of Matrix Theory

TL;DR

This paper introduces a broad class of quarter-BPS solutions in matrix theory that describe non-commutative cylinders with arbitrary profiles, providing a microscopic view of supertube configurations using Bloch wave analysis.

Contribution

It presents a novel method to construct and analyze non-commutative cylindrical solutions in matrix theory via Bloch wave basis, extending understanding of supertube configurations.

Findings

Eigenvalue distributions trace profile curves smoothly

Diagonalization of matrices using Bloch wave basis

Provides microscopic description of supertubes

Abstract

In this note, we present a broad class of quarter-BPS solutions to matrix theory, corresponding to non-commutative cylinders of arbitrary cross-sectional profile in R^8. The solutions provide a microscopic description of a general supertube configuration. Taking advantage of an analogy between a compact matrix dimension and the Hamiltonian of a 1-dimensional crystal, we use a Bloch wave basis to diagonalize the transverse matrices, finding a distribution of eigenvalues which smoothly trace the profile curve as the Bloch wave number is varied.