Emergence of String Monodromy in Effective Field Theory

TL;DR

This paper demonstrates how string monodromy relations naturally emerge in low-energy effective field theories, specifically in the bi-adjoint scalar model, through the imposition of KK and BCJ relations, revealing deep connections between string theory and field theory.

Contribution

The study shows that string monodromy relations can be derived from field theory assumptions in the bi-adjoint scalar model, bridging string and field theory insights.

Findings

Monodromy relations emerge from KK and BCJ relations in BAS EFT.

4-point Z-theory amplitudes are bootstrapped with free parameters.

Analysis depends on factorization and KK-BCJ conditions at 6-point level.

Abstract

String monodromy is a set of linear relations among open string tree amplitudes with different orderings of the vertex operators. In this Letter, we show how these intrinsically stringy relations emerge in low-energy effective field theory from the assumptions of locality and the field theory Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations. Specifically, we study the bi-adjoint scalar model effective field theory (BAS EFT). We impose the field theory KK and BCJ relations on one of the two color-orderings of the BAS EFT amplitudes and show that the second color-ordering has an emergent set of linear relations that, as checked at 4-point to 36-derivative order, are exactly the monodromy relations. The 4-point results depend on a delicate interplay between consistent factorization of 6-point BAS EFT amplitudes and the 6-point KK BCJ conditions. As a consequence of the analysis, the 4-point Z-theory tree amplitudes are bootstrapped up to a symmetric function in $s,t,u$ whose simple exponentiated form has free parameters that capture all the odd zeta values when matched to Z-theory.