Yang-Mills kinematic algebra via homotopy transfer from a worldline operator algebra

TL;DR

This paper derives the kinematic $C_{ infty}$ algebra of Yang-Mills theory from a worldline operator algebra using homotopy transfer, providing a new mathematical perspective on the theory's algebraic structure.

Contribution

It introduces a homotopy transfer method to obtain the kinematic algebra from a worldline operator algebra, linking worldline vertex operators to $L_{ infty}$ structures in Yang-Mills theory.

Findings

Derived the $C_{ infty}$ algebra from a worldline operator algebra.

Provided a homotopy transfer interpretation for worldline vertex operators.

Connected algebraic structures in string-inspired field theories.

Abstract

The homotopy Lie or $L_{\infty}$ algebra encoding Yang-Mills theory is the tensor product of a color Lie algebra with the kinematic $C_{\infty}$ algebra. We derive this $C_{\infty}$ algebra, via homotopy transfer, from a strict operator algebra of a worldline theory, realized as an associative star product algebra. This gives a homotopy transfer interpretation to worldline vertex operators introduced in previous work.