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

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.

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Peter G. Shepard. 2005-11-14. Bloch Waves and Fuzzy Cylinders: 1/4-BPS Solutions of Matrix Theory. https://doi.org/10.1088/1126-6708%2F2006%2F02%2F003

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