Nonperturbative dynamics for abstract $\mathrm{}(p,q)\mathrm{}$ string networks

We describe abstract $\mathrm{}(p,q)\mathrm{}$ string networks which are the string networks of Sen without the information about their embedding in a background spacetime. The non-perturbative dynamical formulation invented for spin networks, in terms of causal evolution of dual triangulations, is applied on them. The formal transition amplitudes are sums over discrete causal histories that evolve $\mathrm{}(p,q)\mathrm{}$ string networks. The dynamics depend on two free $\mathrm{SL}(2,Z)\mathrm{}$ invariant functions which describe the amplitudes for the local evolution moves.