Dimensionless electric displacement in DBI theory ($\mathbf{d}=T_3^{-1}\partial \mathcal{L}/\partial \mathbf{E}$)

With ${\mathbf{E}}_i=2\pi {\alpha }^{\prime }{F}_{0i}$, this normalization separates the nonlinear constitutive relation from the D3-brane tension. It is the normalized canonical electric momentum. The Gauss law constraint in gauge theory requires its divergence to vanish away from string endpoints. On the electric BIon locus it equals the scaled electric field, but this equality is not true for arbitrary configurations.