I understand that when a 10-dimensional superstring theory has a Dp-brane (say, extending in the $x_0, ... , x_p$ directions) we have the total conserved supercharge given by:

\begin{equation} \epsilon_L Q_L + \epsilon_R Q_R \end{equation}

where $Q_L$ and $Q_R$ are the left moving and right moving worldsheet supercharges. This is because the left moving and right moving supercharges aren't conserved by string boundary conditions on the brane, while the sum of these supercharges is conserved. In the above equation we have that the killing spinors are related by:

\begin{equation} \epsilon_L = \Gamma_0 \Gamma_1 ... \Gamma_p \epsilon_R \end{equation}

Each $\epsilon$ is 16-component, so this last equation tells us that each component of $\epsilon_L$ is related to a component of $\epsilon_R$. As a result we only have 16 independent components of the killing spinors, and SUSY is broken in half (from 32 supecharges to 16).

Now going back to $\epsilon_L Q_L + \epsilon_R Q_R$, I would expect this total conserved supercharge to be some 16 component spinor. However, don't the $\epsilon$'s and $Q$'s just contract to give some single value? How can this correspond to a 16-component spinor (total conserved supercharge) that can then be used on supermultiplets?

Also, I get that $\epsilon_L Q_L + \epsilon_R Q_R$ being conserved, together with the fact that $\epsilon_L$ is directly related to $\epsilon_R$, implies that $Q_L$ and $Q_R$ aren't independent; should there not then be some equation, analogous to the second expression above, that relates $Q_L$ directly to $Q_R$?


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