  D$p$-branes acquire effective nonlinear descriptions whose bosonic part is
related to the Born-Infeld action. This nonlinearity has been proven to be a
consequence of the partial ${\cal N}=2\to{\cal N}=1$ supersymmetry breaking,
originating from the solitonic nature of the branes. In this work, we focus on
the effective descriptions of D2-branes. Using the Goldstone multiplet
interpretation of the action and the method of nilpotent ${\cal N}=2$
superfields, we construct the 3D, ${\cal N}=1$ superspace effective action
which makes the first supersymmetry manifest and realizes the second,
spontaneously broken, supersymmetry nonlinearly. We show that there are two
such supersymmetric extensions of the 3D Born-Infeld action which correspond to
the dynamics of the 3D Maxwell-Goldstone multiplet and the 3D projection of the
Tensor-Goldstone multiplet respectively. Moreover, we demonstrate that these
results are derived by applying the constrained superfield approach on the
${\cal N}=2, D=3$ vector and chiral multiplets after expanding them around a
nontrivial vacuum. We find that these two descriptions are related by a duality
transformation which results in the inversion of a dimensionless parameter. For
both descriptions we derive the explicit bosonic and fermionic parts of the 3D
super Born-Infeld action. Finally, consider the deformation of the
Maxwell-Goldstone superspace action by the characteristic Chern-Simons-like,
gauge invariant, mass term.

High Energy Physics - Theory