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

Peter G. Shepard

doi:10.1088/1126-6708/2006/02/003

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

High Energy Physics - Theory 2009-11-11 v3

Authors: Peter G. Shepard

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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.

Keywords

matrix theory quarter-BPS solutions non-commutative cylinders supertubes Bloch waves fuzzy geometry

Cite

@article{arxiv.hep-th/0510127,
  title  = {Bloch Waves and Fuzzy Cylinders: 1/4-BPS Solutions of Matrix Theory},
  author = {Peter G. Shepard},
  journal= {arXiv preprint arXiv:hep-th/0510127},
  year   = {2009}
}