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

Abstract

We examine universal positivity constraints on 2 → 2 scattering in 4d planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory with higher-derivative corrections. We present numerical evidence that the convex region of allowed Wilson coefficients (the “EFT-hedron”) flattens completely along about one-third of its dimensions when an increasing number of constraints on the spectral density from crossing-symmetry are included. Our analysis relies on the formulation of the positivity constraints as a linear optimization problem, which we implement using two numerical solvers, SDPB and CPLEX. Motivated by the flattening, we propose a novel partially resummed low-energy expansion of the 2 → 2 amplitude. As part of the analysis, we provide additional evidence in favor of the conjecture [1] that the Veneziano amplitude is the only amplitude compatible with both S-matrix bootstrap constraints and string monodromy.

Weak-gravity bound in asymptotically safe gravity-gauge systems

“…By now positivity bounds have been derived in a variety of contexts, including without and with gravity, see, e.g., [72][73][74][75][76][77][78] and with [79][80][81][82][83][84][85][86][87] respectively, and [88] for reviews. The impact of broken Lorentz invariance has been considered in [89][90][91] and in a quantum gravitational context, positivity bounds have been considered in string theory [92][93][94]. In order to make use of results on photon self-interactions in asymptotically safe gravity [95][96][97], we focus on positivity bounds for the photon [1,[98][99][100].…”