Classical algebraic structures in string theory effective actions

TL;DR

This paper develops a general framework for deriving effective actions in string theory by integrating out massive modes, applying it to open bosonic string field theory, and exploring implications for gauge theories and D-brane deformations.

Contribution

It introduces a systematic method for composing and deforming effective actions in string field theories based on cyclic homotopy algebras, with explicit applications to open bosonic strings.

Findings

Systematic integration of massive modes yields non-abelian $A_ infty$-gauge theories.

Vertical decomposition constructs effective open-closed couplings via deformations.

Framework aids in understanding D-brane deformations and tadpole removal.

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 $A_\infty$ 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.