Stringy Completions of the Standard Model from the Bottom Up

TL;DR

This paper explores string-inspired amplitude ans"atze for the Standard Model and gauge theories, revealing bounds on gauge group ranks, the necessity of graviton exchange for unitarity, and constraints linking Standard Model parameters to fundamental scales.

Contribution

It introduces string-inspired amplitude ans"atze for 2-to-2 scattering, deriving bounds on gauge group ranks and connecting Standard Model couplings with string and Planck scales.

Findings

Maximum gauge group rank in 4D is 24.

Gauge group rank bound in dimensions 5-10 aligns with swampland conjecture.

Unitarity requires graviton exchange in the ans"atze.

Abstract

We study a class of tree-level ans\"atze for $2\to 2$ scalar and gauge boson amplitudes inspired by stringy UV completions. These amplitudes manifest Regge boundedness and are exponentially soft for fixed-angle high energy scattering, but unitarity in the form of positive expandability of massive residues is a nontrivial consistency condition. In particular, unitarity forces these ans\"atze to include graviton exchange. In the context of gauge boson scattering, we study gauge groups $SO(N)$ and $SU(N)$. In four dimensions, the bound on the rank of the gauge group is $24$ for both groups, and occurs at the maximum value of the gauge coupling $g_{YM}^2 = \frac{2M_s^2}{ M_P^2} $. In integer dimensions $ 5\leq D \leq 10$ , we find evidence that the maximum allowed allowed rank $r$ of the gauge group agrees with the swampland conjecture $r < 26-D$. The bound is surprisingly identical for both $SU(N)$ and $SO(N)$ in integer spacetime dimensions. We also study the electroweak sector of the standard model via $2 \to 2$ Higgs scattering and find interesting constraints relating standard model couplings, the putative string scale, and the Planck scale