Homotopy transfer and effective field theory II: strings and double field theory

Abstract

We continue our study of effective field theory via homotopy transfer ofL∞-algebras, and apply it to tree-level non-Wilsonian effective actions of thekind discussed by Sen in which the modes integrated out are comparable inmass to the modes that are kept. We focus on the construction of effectiveactions for string states at fixed levels and in particular on the construction ofweakly constrained double field theory. With these examples in mind, wediscuss closed string theory on toroidal backgrounds and resolve some subtleissues involving vertex operators, including the proper form of cocycle factorsand of the reflector state. This resolves outstanding issues concerning theconstruction of covariant closed string field theory on toroidal backgrounds.The weakly constrained double field theory is formally obtained from closedstring field theory on a toroidal background by integrating out all but the‘doubly massless’ states and homotopy transfer then gives a prescription fordetermining the theory’s vertices and symmetries. We also discuss consistenttruncation in the context of homotopy transfer.