Junctions of Supersymmetric Tubes
Dongsu Bak, Sang-Woo Kim
TL;DR
Bak and Kim study noncommutative supersymmetric tubular configurations within the BFSS matrix model, focusing on worldvolume gauge data, charges, and RR dipole moments carried by tubes. They derive BPS tube solutions with algebra $[z,x]=i l y$, $[y,z]=i l x$, $[x,y]=0$, characterized by radius $\rho$ and noncommutativity scale $l$, and compute the associated electric/magnetic fields, D0 density, and F-string content, finding consistency with supergravity and preserving 1/4 of the supersymmetry. The work analyzes fluctuations around multiple tubes and tube-D0 systems, obtaining spectra for concentric tubes and tube-D0 strings, and identifies symmetry-breaking patterns and mass formulas for stretched strings. They introduce local operations—junctions, bends, and NC-scale changes—that can be composed to realize arbitrary Riemann-surface-like tube configurations with varying noncommutativity, interpreting junctions as domain walls between $U(1)$ and $U(2)$ (and more generally) noncommutative worldvolume gauge theories. The conclusions highlight a versatile construction framework for complex tubular geometries in string/M-theory, while noting open dynamical questions and limits of current understanding, including force cancellation and NCOS behavior.
Abstract
We begin by reviewing the noncommutative supersymmetric tubular configurations in the matrix theory. We identify the worldvolume gauge fields, the charges and the moment of R-R charges carried by the tube. We also study the fluctuations around many tubes and tube-D0 systems. Based on the supersymmetric tubes, we have constructed more general configurations that approach supersymmetric tubes asymptotically. These include a bend with angle and a junction that connects two tubes to one. The junction may be interpreted as a finite-energy domain wall that interpolates U(1) and U(2) worldvolume gauge theories. We also construct a tube along which the noncommutativity scale changes. Relying upon these basic units of operations, one may build physical configurations corresponding to any shape of Riemann surfaces of arbitrary topology. Variations of the noncommutativity scale are allowed over the Riemann surfaces. Particularly simple such configurations are Y-shaped junctions.