The paper proves, from massive spin-2 scattering sum rules, that the lightest KK graviton must couple to a scalar with (m_sc/m_1)^2 ≤ 4/3, and every KK graviton m_n to a scalar with (m_sc/m_n)^2 < 36/25.
Weyl bound for trilinear periods via conformal bootstrap
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Let $f_1,f_2$ be holomorphic modular forms of the same weight for a cocompact lattice $\Gamma < \mathrm{PSL}_2(\mathbf{R})$. We estimate the rate of decay of the coefficients in the expansion of $f_1\overline{f_2}$ in a Laplace eigenbasis. By specializing our main theorem to the case where $\Gamma$ is arithmetic, we obtain new instances of the Weyl bound for triple product $L$-functions in the spectral aspect. Our method builds on the conformal bootstrap in physics.
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Moduli Bounds from Spin-2 Sum Rules
The paper proves, from massive spin-2 scattering sum rules, that the lightest KK graviton must couple to a scalar with (m_sc/m_1)^2 ≤ 4/3, and every KK graviton m_n to a scalar with (m_sc/m_n)^2 < 36/25.