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Mnev, I. V.; Ulanovskii, М. V.

doi:10.1023/a:1020127204766

Cited by 1 publication

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“…Aspects of the relation between integrating out degrees of freedom and homotopy transfer appear to have been known to experts, with instances of this relation being explored for particular models in e.g. [6–8], and in the

A_{\infty }

framework relevant for open string theory in [9, 10], but to the best of our knowledge it was only in [1, 4, 5] that the role of homotopy transfer for general field theories requiring

L_{\infty }

‐algebras has been discussed explicitly. Apart from being of conceptual interest, this relation is of importance for applications starting from (classical) closed string field theory, which in Zwiebach's covariant formulation is governed by an

L_{\infty }

‐algebra [11].…”

Section: Introductionmentioning

confidence: 99%

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

Arvanitakis

Hohm

Hull

et al. 2022

Fortschritte der Physik

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We continue our study of effective field theory via homotopy transfer of L∞$L_\infty$‐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.

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A_{\infty }

framework relevant for open string theory in [9, 10], but to the best of our knowledge it was only in [1, 4, 5] that the role of homotopy transfer for general field theories requiring