Nonperturbative dynamics for abstract (p,q) string networks

TL;DR

This paper develops a nonperturbative dynamical framework for abstract (p,q) string networks, using a causal evolution approach similar to spin networks, with dynamics governed by SL(2,Z) invariant functions.

Contribution

It introduces a novel nonperturbative formulation for (p,q) string networks based on causal evolution of dual triangulations, extending spin network techniques.

Findings

Formal transition amplitudes as sums over discrete causal histories

Dynamics depend on two SL(2,Z) invariant functions

Framework applicable to abstract string networks without background embedding

Abstract

We describe abstract (p,q) 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 to them. The formal transition amplitudes are sums over discrete causal histories that evolve (p,q) string networks. The dynamics depend on two free SL(2,Z) invariant functions which describe the amplitudes for the local evolution moves.