Reciprocal Non-Relativistic Decoupling Limits of String Theory and M-Theory

It has recently been realised that there are supersymmetry-preserving non-relativistic decoupling limits associated with each half-BPS object in String Theory and M-Theory. We argue that, given a $p$-brane and a $q$-brane for which there is a quarter-BPS intersecting configuration, the $p$-brane decoupling limit of the $q$-brane's worldvolume QFT is necessarily equal to the reciprocal $q$-brane decoupling limit of the $p$-brane's worldvolume theory. This is explicitly shown for the cases of the D0-D4 and D1-D3 systems. As an application of this idea, we use the reciprocal pair of limits in the M2-M5 system to describe the dynamics of interacting self-dual strings in the six-dimensional $\mathcal{N}=(2,0)$ theory. We also discuss the limits of the dual gravitational theories and, using symmetries, argue that the duality is maintained by the limits.