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 $A_\infty$ or $L_\infty$ 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 $A_\infty$-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-branes deformations induced by changes in the closed string background.

中文翻译：

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弦论中的经典代数结构有效作用

我们研究了基于 $A_\infty$ 或 $L_\infty$ 类型的循环同伦代数从弦场理论中经典地整合出大量激发而获得的弦理论有效作用的一般性质。我们在 UV 理论中构建了可观测值，并讨论了它们在集成后的命运。此外，我们讨论了如何组合两个后续的自由度积分（水平组合）以及如何在使用新的一致相互作用（垂直分解）变形 UV 理论后积分出自由度。然后，我们使用 Witten 的开放弦场理论将我们的一般结果应用于开放玻色弦。在那里，我们展示了如何使用水平合成从一组无质量激发中系统地整合出 Nakanishi-Lautrup 场，以开放弦胶子的非阿贝尔 $A_\infty$-规范理论结束。此外，我们展示了如何通过使用 Ellwood 不变量给出的蝌蚪使 Witten OSFT 变形来使用垂直分解来构建有效的开闭耦合。此外，我们讨论了有效理论如何控制微观理论中去除蝌蚪的可能性，为研究由闭合弦背景变化引起的 D 膜变形提供了新的框架。