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<p>We derive analytic constraints on the weakly-coupled spectrum of theories with a massless scalar under the standard assumptions of the S-matrix bootstrap program. These bootstrap bounds apply to any theory (with or without gravity) with fully crossing symmetric (i.e. <i>stu</i>-symmetric) four-point amplitudes and generalize results for color- or flavor-ordered (i.e. <i>su</i>-symmetric) planar amplitudes recently proved by one of the authors. We assume that the theory is weakly-coupled below some cut-off, that the four-point massless scalar amplitude is polynomially-bounded in the Regge limit, and that this amplitude exchanges states with a discrete set of masses and a finite set of spins at each mass level. The spins and masses must then satisfy “Sequential Spin Constraints” (SSC) and “Sequential Mass Constraints” (SMC). The SSC requires the lightest spin-<i>j</i> state to be lighter than the lightest spin-(<i>j</i> + 1) state (in the <i>su</i>-symmetric case) or the lightest spin-(<i>j</i> + 2) state (in the <i>stu</i>-symmetric case). The SMC requires the mass of the lightest spin-<i>j</i> state to be smaller than some non-linear function of the masses of lower-spin states. Our results also apply to super-gluon and super-graviton amplitudes stripped of their polarization dependence. In particular, the open and closed superstring spectra saturate the SSC with maximum spins <i>J</i><sub><i>n</i>,open</sub> = <i>n</i> + 1 and <i>J</i><sub><i>n</i>,closed</sub> = 2<i>n</i> + 2, respectively, at the <i>n</i><sup>th</sup> mass level.</p>

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Analytic bootstrap bounds on masses and spins in gravitational and non-gravitational scalar theories

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  • 发表日期：

    2025年6月17日

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  • Justin Berman,
  • Nicholas Geiser

摘要

We derive analytic constraints on the weakly-coupled spectrum of theories with a massless scalar under the standard assumptions of the S-matrix bootstrap program. These bootstrap bounds apply to any theory (with or without gravity) with fully crossing symmetric (i.e. stu-symmetric) four-point amplitudes and generalize results for color- or flavor-ordered (i.e. su-symmetric) planar amplitudes recently proved by one of the authors. We assume that the theory is weakly-coupled below some cut-off, that the four-point massless scalar amplitude is polynomially-bounded in the Regge limit, and that this amplitude exchanges states with a discrete set of masses and a finite set of spins at each mass level. The spins and masses must then satisfy “Sequential Spin Constraints” (SSC) and “Sequential Mass Constraints” (SMC). The SSC requires the lightest spin-j state to be lighter than the lightest spin-(j + 1) state (in the su-symmetric case) or the lightest spin-(j + 2) state (in the stu-symmetric case). The SMC requires the mass of the lightest spin-j state to be smaller than some non-linear function of the masses of lower-spin states. Our results also apply to super-gluon and super-graviton amplitudes stripped of their polarization dependence. In particular, the open and closed superstring spectra saturate the SSC with maximum spins Jn,open = n + 1 and Jn,closed = 2n + 2, respectively, at the nth mass level.