Noncommutative Supersymmetric Tubes

TL;DR

This work tackles the problem of realizing supersymmetric tubular D-brane configurations within matrix theory and understanding their worldvolume dynamics. It derives BPS equations $[X,Y]=0$, $D_0 Z=0$, $D_0 X \pm i[Z,X]=0$, $D_0 Y \pm i[Z,Y]=0$ and shows they admit a noncommutative cylinder solution with radius $\rho$ and noncommutativity $l$, described by $[z,x]= i l y$, $[y,z]= i l x$, $[x,y]=0$ and a $*$-product on the tube. The paper then analyzes fluctuations, showing the worldvolume theory is a twisted, spacelike noncommutative gauge theory on a cylinder with a Chern-Simons term, and constructs D0 solitons via shift operators, as well as configurations of multiple tubes yielding a $U(p)$ NC gauge theory. Overall, the results provide a concrete NC gauge-theoretic description of supersymmetric tubes and their D0 excitations in matrix theory, with connections to Born-Infeld supertubes and potential conformal field theory descriptions for deeper dynamical insight.

Abstract

We investigate supersymmetric tubular configurations in the matrix theory. We construct a host of BPS configurations of eight supersymmetries. They can be regarded as cylindrical D2 branes carrying nonvanishing angular momentum. For the simplest tube, the world volume can be described as noncommutative tube and the world volume dynamics can be identified as a noncommutative gauge theory. Among the BPS configurations, some describe excitations on the tube and others describe many parallel tubes of different size and center.