Negative running of gravitational positivity

Abstract

We investigate the one-loop renormalization group evolution in four dimensions of the leading operators in the effective field theories of shift-symmetric scalars, photons, and gravitons. We show that certain non-minimal three-point interactions induce a negative running of the corresponding Wilson coefficients, with beta-functions suppressed by the Planck scale. The decrease of the coefficients toward the infrared prompts us to revisit their dispersive bounds, in particular accounting for graviton loops. Gravitational interactions generate positive infrared contributions which, after smearing over the momentum transfer, are argued to dominated over the negative running, provided the number of non-minimally coupled particles is bounded from above according to the species bound.

Figures (6)

• Figure 1: Cut diagrams contributing to the anomalous dimension of the leading four-scalar EFT coefficient. Eqs. (), (), (), and () correspond, respectively, to the top-left, top-right, bottom-left, and bottom-right cuts. $\Phi = \phi, \sigma_i, \chi_i, V_i, h$ in the top-left cut.
• Figure 2: Cut diagrams contributing to the anomalous dimension of the leading (MHV) four-photon EFT coefficient. $\Phi = \sigma_i, \chi_i, V_i, h$ in the top-left cut and $\Phi' = \sigma, \chi, V$ in the top-right and middle-left cuts. The top-right cut also includes contributions with $\Phi_i, \bar{\Phi}'_j = \gamma^+, V_j^-$ and $\Phi_i, \bar{\Phi}'_j = V_i^+, \gamma^-$, and the bottom-right cut contributions with $V_i^\pm = \gamma^-$.
• Figure 3: Cuts that contribute to the anomalous dimension of the leading (MHV) four-graviton EFT coefficient. $\Phi' = \sigma, V$ in the middle-left.
• Figure 4: Cut diagram involving the $t$-channel exchange of a minimally coupled graviton, responsible for the negative running of the leading four-scalar EFT coefficient.
• Figure 5: Contour of integration $C$ in the complex $s$ plane associated with the dispersion relations Eq. (), along with the non-analyticities of the integrand.