# HEP/Astro Journal Club -- Friday, 05 April 2002

##
D-branes as solitons of an `N`=1, `D`=10
non-commutative gauge theory

## Abstract

We consider a D3 brane within a D9 brane in the presence of a
B-field whose polarization is transverse to the D3 brane. Using the
Green-Schwarz formulation we study the supersymmetry of the configuration by
examining the surface terms. It is found that there is residual supersymmetry
only when the B-field satisfies a certain condition.

Then we turn to another description of the same system via an N=1 D=10
gauge theory. This is in the spirit of the works of Witten and Douglas who
observed that the instanton solutions of a Dp brane world volume theory can be
identified as D(p-4) branes within the Dp branes. In the present case the
gauge theory becomes non-commutative (NC) in its six dimensions due to the
presence of the B-field. Using the NC techniques one can
write down, in abstract notations, the soliton solutions of the six dimensinal
NC gauge theory, which can be uplifted to ten dimensions. We show that the
supersymmetry preserved by the solutions is the same as before.

Therefore the result can be viewed as a generalization of the work of Witten
and Douglas.

## References

M. Mihailescu, I. Y. Park and T. A. Tran,
*“D-branes as solitons of an *`N`=1,
`D`=10 non-commutative gauge theory,”
Phys. Rev. D **64**, 046006 (2001)
[hep-th/0011079]

E. Witten, *“BPS bound states of D0-D6 and D0-D8 systems
in a B-field,”*
hep-th/0012054.

## 12:30, Smith Lab 4079

George T. Fleming
(
gfleming@mps.ohio-state.edu
),
last updated 04 March 2002.