Moduli Bounds from Spin-2 Sum Rules

Abstract

Mirbabayi and Villadoro have provided strong numerical evidence for a universal upper bound on the mass of the lightest scalar field in gravitational Kaluza--Klein (KK) theories. This bound states that the lightest KK graviton, with mass $m_1$, must couple to at least one scalar with mass $m_{\mathrm{sc}}$ such that $(m_{\mathrm{sc}}/m_1{)}^2\le 4/3$. We give a proof of this bound using the approach of the conformal bootstrap applied to sum rules for massive spin-2 scattering amplitudes. We additionally show that each heavier KK graviton, with mass $m_n$, must couple to at least one scalar with mass $m_{\mathrm{sc}}$ such that $(m_{\mathrm{sc}}/m_n{)}^2<36/25$.

9 pages