Homotopy Transfer and Effective Field Theory II: Strings and Double Field Theory

TL;DR

This paper advances the understanding of effective field theories in string theory by applying homotopy transfer to construct weakly constrained double field theory and resolving key issues in covariant closed string field theory on toroidal backgrounds.

Contribution

It introduces a novel application of homotopy transfer to derive effective actions for string states and clarifies the construction of covariant double field theory on toroidal backgrounds.

Findings

Constructed effective actions for string states at fixed levels.

Resolved issues with vertex operators and cocycle factors.

Provided a homotopy transfer framework for double field theory.

Abstract

We continue our study of effective field theory via homotopy transfer of $L_\infty$-algebras, and apply it to tree-level non-Wilsonian effective actions of the kind discussed by Sen in which the modes integrated out are comparable in mass to the modes that are kept. We focus on the construction of effective actions for string states at fixed levels and in particular on the construction of weakly constrained double field theory. With these examples in mind, we discuss closed string theory on toroidal backgrounds and resolve some subtle issues involving vertex operators, including the proper form of cocycle factors and of the reflector state. This resolves outstanding issues concerning the construction of covariant closed string field theory on toroidal backgrounds. The weakly constrained double field theory is formally obtained from closed string field theory on a toroidal background by integrating out all but the doubly massless' states and homotopy transfer then gives a prescription for determining the theory's vertices and symmetries. We also discuss consistent truncation in the context of homotopy transfer.