D-branes as Solitons of an N=1, D=10 Non-commutative Gauge Theory

TL;DR

The paper analyzes a D3-D9 brane system with a transverse B-field and demonstrates that the resulting SUSY-breaking pattern matches that of a soliton in a six-dimensional noncommutative gauge theory obtained by dimensional reduction from a ten-dimensional $N=1$ theory, identifying the soliton as the D3-brane's low-energy realization. By constructing solitons in the reduced noncommutative gauge theory and comparing the SUSY conditions, the authors show a precise equivalence with the open-string boundary-condition analysis, supporting the brane-as-soliton picture. Fluctuation analysis indicates no tachyons for the SUSY-preserving noncommutativity, reinforcing the stability of the D3-brane soliton in this setup. These results extend earlier lower-codimension observations and strengthen the link between D-branes and noncommutative gauge theory solitons in transverse B-field backgrounds.

Abstract

We consider a Dp brane within a D9 brane in the presence of a B-field whose polarization is {\em transverse} to the Dp brane. To be definite, we take a D3-D9 system. It is observed that the system has the same pattern of supersymmetry breaking as that of a soliton of the six dimensional non-commutative gauge theory that is obtained by dimensional reduction of an {\cal N}=1, D=10 gauge theory. These results indicate that the soliton solution is the low energy realization of a D3 brane in a D9 brane with a transverse B-field, hence can be viewed as a generalization of the previous results in the literature where similar observations were made for lower codimensional cases.