BPS Bound States Of D0-D6 And D0-D8 Systems In A B-Field

TL;DR

The paper investigates D0–D6 and D0–D8 brane systems in Type IIA string theory with a constant $B$-field, showing that supersymmetry can be restored on codimension-one loci and that $1/8$-BPS bound states may exist on one side of these loci. When compactified on ${\bf T}^6$, the number of $1/8$-BPS states can jump as vacuum moduli vary, with the large-$B$ limit admitting a noncommutative Yang–Mills description of the bound states. The analysis combines worldsheet spectrum (Ramond/NS sectors), low-energy quantum-mechanical dynamics with a Fayet–Iliopoulos parameter $r$, and a noncommutative Yang–Mills perspective to connect SUSY conditions to bound-state existence. The results extend to configurations with multiple D0-branes and D6-branes, yielding an ADHM-like moduli space structure and a precise moduli-space description of SUSY ground states; in the D0–D8 case, a second SUSY locus and a corresponding bound state are similarly characterized. Overall, the work links brane-bound-state physics, moduli-space geometry, and noncommutative field theory in a coherent framework for understanding BPS state counting and stability in string compactifications.

Abstract

The D0-D6 system, which is not supersymmetric in the absence of a Neveu-Schwarz B-field, becomes supersymmetric if a suitable constant B-field is turned on. On one side of the supersymmetric locus, this system has a BPS bound state, and on the other side it does not. After compactification on T^6, this gives a simple example in which the number of 1/8 BPS states jumps as the moduli of the compactification are changed. The D0-D8 system in a B-field has two different supersymmetric loci, only one of which is continuously connected to the familiar supersymmetric D0-D8 system without a B-field. In a certain range, the D0-D8 system also has a BPS bound state. In the limit in which the B-field goes to infinity, supersymmetric D0-D6 and D0-D8 systems and their bound states can be studied using noncommutative Yang-Mills theory.