L∞-structure and scattering amplitudes of antisymmetric tensor gauge field theory

Abstract

We explore the $L_{\infty }$-algebraic structures in antisymmetric tensor gauge field theory, focusing on the construction of a contracting homotopy for the chain map between two distinct $L_{\infty }$-algebras. Utilizing the free Feynman propagators, we establish a quasi-isomorphism between the original $L_{\infty }$-algebra and its minimal model. This construction leads to the recursive relations for the coefficients of Berends-Giele-like currents which are essential in the computations of tree-level scattering amplitudes of tensor gauge fields. Under such framework, we derive the generating functional for all tree-level amplitudes in terms of Maurer-Cartan elements within the minimal model. As an illustration, we carry out the three- and four-point scattering amplitudes in the tensor gauge theory by applying field operators to the Maurer-Cartan action with appropriate boundary conditions.