Abstract
We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of A∞ or L∞ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten’s open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian A∞-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-brane deformations induced by changes in the closed string background.
Highlights
In recent years complete constructions of super string field theories have become available [1,2,3,4,5,6,7] and there has been interest in explicitly computing the effective action of a given microscopic string field theory, after integrating out the massive degrees of freedom [8,9,10,11], as originally done in [12]
We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of A∞ or L∞ type
In this paper we have analyzed several aspects of string field theory effective actions whose gauge invariance is encoded in homotopy structures of A∞ or L∞ type
Summary
In recent years complete constructions of super string field theories have become available [1,2,3,4,5,6,7] and there has been interest in explicitly computing the effective action of a given microscopic string field theory, after integrating out the massive degrees of freedom [8,9,10,11], as originally done in [12]. The process of projecting out a set of fields in the tensor algebra can be rephrased as a strong-deformationretract (SDR) [48] and the final form of the effective vertices is directly implied by the homological perturbation lemma [53,54,55] which describes how the SDR for the initially free theory is deformed by switching on interactions This nicely parallels what we have obtained by directly solving the equations of motion for the massive fields by automatically encoding in the co-algebra language all the tree-level Feynman diagrams. It is often useful to consider deformations of the original UV action that preserve the homotopy structure and the gauge invariance This is for example what happens by adding to the action an observable of the kind discussed above whose defining odd coderivation e is nilpotent, so that (m + μe)2 = 0. Parallel considerations can be applied to a cyclic L∞ structure, and the details are presented in appendix B
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