HEFT Numerators from Kinematic Algebra

TL;DR

This paper derives gauge-invariant kinematic numerators for heavy-mass effective field theory using string theory vertex operator algebra, organizing contributions via rooted trees and connecting to string theory fusion rules.

Contribution

It introduces a novel derivation of kinematic numerators from string theory correlators, providing a deeper algebraic understanding of heavy-mass effective field theory.

Findings

Kinematic numerators expressed as correlators of nested commutators.

Numerators organized using rooted tree structures.

Connection established between string theory fusion rules and field theory numerators.

Abstract

We derive the kinematic numerator factors for heavy-mass effective field theory from the field theory limit of the string theory vertex operator kinematic algebra introduced in arXiv:1806.09584. The kinematic numerators are derived as correlators of nested commutators of gluon vertex operators evaluated between massive tachyonic vertex operators. The resulting numerators are given by products of structure constants of the vertex operator algebra which yield gauge invariant expressions. The computation of the nested commutators leads to a natural organisation in the form of rooted trees, endowed with an order that facilitates the enumeration of the various contributions. This kinematic algebra gives a string theory understanding of the field theory fusion rules for constructing the heavy-mass effective field theory numerator of arXiv:2104.11206 and arXiv:2111.15649.