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Rise of Linear Regge Trajectories

Yu-tin Huang1,2,3, Sara Ricossa4, Francesco Riva4, and Jie-Da Tsai1

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Phys. Rev. Lett. 137, 041603 – Published 24 July, 2026

DOI: https://doi.org/10.1103/byzm-k9lw

Abstract

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.

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Phys. Rev. Lett. 137, 041603– Published 24 July, 2026
  • Received 23 October 2025
  • Revised 20 May 2026
  • Accepted 21 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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