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

The homotopy Lie or <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>L</a:mi> <a:mo>∞</a:mo> </a:msub> </a:math> algebra encoding Yang-Mills theory is the tensor product of a color Lie algebra with the kinematic <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>C</c:mi> <c:mo>∞</c:mo> </c:msub> </c:math> algebra. We derive this <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>C</e:mi> <e:mo>∞</e:mo> </e:msub> </e:math> 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.