(p,q) string ($T_{p,q}=\frac{1}{2\pi {\alpha }^{\prime }}\sqrt{p^2+q^2/g_s^2}(C_0=0)$)

A (p,q) string carries $p$ units of fundamental string charge and $q$ units of D1-brane charge. Coprime integers label an elementary primitive charge vector; nonprimitive vectors describe multiple units. The displayed tension uses the string metric and vanishing axion. In the M-theory torus duality, it comes from an M2-brane wrapped on the corresponding primitive one-cycle.

At a junction of (p,q) strings, their oriented charge vectors sum to zero. A static junction also balances the tension vectors. Supersymmetry further correlates spatial directions with charge phases so that the arms share kappa symmetry projectors. Additional independent conditions reduce the common Killing spinor space; an aligned dyonic string alone does not reduce its fraction relative to an aligned fundamental string.

// Target: geometry-and-topology.bigb