In 'Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory', Gaiotto and Witten derive boundary conditions for the worldvolume theory of the D3 brane. In particular the boundary conditions (see pages 8-10) on the fermionic field $\Psi$ is $ \Gamma_3\Psi=\Psi' \otimes \vartheta $ where $\Psi'$ transforms under the boundary Lorentz and R-symmetry, while $$\vartheta= \begin{pmatrix} a \\ 1\end{pmatrix},$$ up to scaling.

It is stated later on below equation (4.32) that the choices $a=\infty$ and $a=0$ correspond to NS5-brane and NS5-antibrane boundary conditions.

My question is, how does one discern which value of $a$ corresponds to NS5-brane or NS5-antibrane? Can this even be determined, or is the notion of brane and antibrane only defined relative to each other in this case?


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