Rise of Linear Regge Trajectories.

In this Letter, we consider constraints on the low-energy spectrum of scalar amplitudes with higher-spin exchanges. Assuming unitarity, crossing symmetry, and superconvergent high energy behavior, we demonstrate that the spectrum that maximizes the leading higher spin couplings of the second and third resonances is consistently given by a linear trajectory. We work strictly in ten dimensions although we expect analysis in other dimensions to be similar. For gravitational theories, the optimal spectrum is the linear trajectory defined by the mass and spin of the graviton and the lightest spin-4 resonance.