Bootstrapping string models with entanglement minimization and machine learning

We present a new approach to bootstrapping stringlike theories by exploiting a local crossing symmetric dispersion relation and field redefinition ambiguities. This approach enables us to use mass-level truncation and to go beyond the dual resonance hypothesis. We consider both open and closed strings, focusing mainly on open tree-level amplitudes with an integer-spaced spectrum, and two leading Wilson coefficients as inputs. Using entanglement minimization in the form of the minimum of the first finite moment of linear entropy or entangling power, we get an excellent approximation to the superstring amplitudes, including the leading and subleading Regge trajectories. We find other interesting S matrices that do not obey the duality hypothesis, but exhibit a transition from Regge behavior to power law behavior in the high energy limit. Finally, we also examine machine-learning techniques to do bootstrap and discuss potential advantages over the present approach.