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Homotopy Transfer and Effective Field Theory II: Strings and Double Field Theory
Author(s) -
Arvanitakis Alex S.,
Hohm Olaf,
Hull Chris,
Lekeu Victor
Publication year - 2022
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.202200004
Subject(s) - string field theory , homotopy , covariant transformation , relationship between string theory and quantum field theory , string theory , theoretical physics , field (mathematics) , non critical string theory , context (archaeology) , vertex (graph theory) , physics , mathematics , field theory (psychology) , pure mathematics , mathematical physics , quantum mechanics , discrete mathematics , quantum gravity , graph , paleontology , quantum , biology
Abstract We continue our study of effective field theory via homotopy transfer ofL ∞ $L_\infty$ ‐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.