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

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arxiv 2412.17902 v2 pith:UY5KBXAB submitted 2024-12-23 hep-th hep-ph

Justin Berman , Nicholas Geiser This is my paper
classification hep-thhep-ph
keywords symmetriclightestmassmassesspin-spinsstateamplitudes
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

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 ${J_{n,\text{open}} = n+1}$ and ${J_{n,\text{closed}} = 2n+2}$, respectively, at the $n^\text{th}$ mass level.

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