Causality constraints on corrections to Einstein gravity

Abstract

We study constraints from causality and unitarity on 2 → 2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G → 0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

Gravitational Regge bounds

“…19 In writing (18) and (19) we took into account the fact that A and B are nonidentical particles. 20 The situation in d = 5 is analogous to the simple example discussed in [49]. 21 In the gapped theories the situation is exactly the same [50].…”

“…5 In the most conservative Born model and d = 5, it requires that b > 0. 6 This point has been recently emphasized in [20]. 7 In the context of AdS/CFT the corresponding bound is related to the bound on chaos, see appendix A in [26].…”

“…As we review in Appendix B, it readily follows from (17) that the partial wave expansion converges pointwise for −1 < cos θ < 1 in d > 5, and converges as a distribution in d = 5. 20 A simple way to understand the convergence of the partial wave expansion is to inspect the large J behavior of the sum (18). As J becomes large the partial wave integral (19) effectively localizes close to t = 0 due to the oscillatory nature of the Legendre polynomials and therefore the small t expansion (17) translates to the large J expansion.…”

Flattening of the EFT-hedron: supersymmetric positivity bounds and the search for string theory

“…Among possible future directions, it would be especially interesting to investigate how one might isolate string theory in the N = 4 supersymmetric EFT-hedron in a more generic way. Other than imposing monodromy (or that the low-energy amplitude must satisfy some double- 17 The Veneziano amplitude can also be written as A str [zz z z] = (α ′ s) 2 sin(πα ′ t) π Γ(−α ′ s)Γ(−α ′ t)Γ(−α ′ u). (7.17) In this form, its low-energy expansion takes the form of (7.13) with some particular set of ã′ k,q coefficients.…”

“…These basic high-energy assumptions facilitate a dispersive representation of the Wilson coefficients which implies that they must lie in a convex region sometimes called the "EFT-hedron" [2]. The allowed region of Wilson coefficients has been explored recently for theories of massless particles, including for scalars [2][3][4], massless pions [5][6][7][8][9][10], photons [11][12][13][14][15], and gravitons [16,17].…”