Quantum action for heterotic string field theory with quantum L-infinity structure

Abstract

We construct a quantum action for heterotic string field theory that satisfies the quantum Batalin-Vilkovisky equation. Assuming a triangulation of the bosonic moduli space, the prescription for inserting picture-changing operators is determined based on a quantum L-infinity structure. After concretely constructing some of the lower-order interactions, we propose a general prescription, which generalizes that for constructing the classical interactions governed by a classical L-infinity structure. Assuming it does not suffer from spurious poles, all quantum interactions are determined by iteratively solving differential equations and transforming the solutions via IBL-infinity-transfer. To demonstrate the consistency of our prescription, we compute the one-loop two-point functions (modulo the spurious pole issue) and show that they agree with those in the first-quantized formulation.