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.
Working within the framework of both the A ∞ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter. For a specific class of backgrounds, we find that this condition localizes on the boundary of the worldsheet moduli space, thus providing a very simple computational prescription for recovering algebraic constraints (generalized ADHM equations) which need to be satisfied by the moduli. Applying our results to the D(−1)/D3 system, we confirm up to third order that blowing up the size of the D-instanton inside the D3 brane worldvolume is an exact modulus of the full string theory. We also discuss examples of more complicated backgrounds, such as instantons on unresolved ALE spaces, as well as the spiked instantons. ArXiv ePrint: 1910.00538 A Spinors in 4d 55 B Conventions for the A ∞ OSFT 56 C Some useful OPE and correlators 58
We analyze the inspiral dynamics of equal-mass precessing black-hole binaries using multi-timescale techniques. The orbit-averaged post-Newtonian evolutionary equations admit two constants of motion in the equal-mass limit, namely the magnitude of the total spin S and the effective spin ξ. This feature makes the entire dynamics qualitatively different compared to the generic unequalmass case, where only ξ is constant while the variable S parametrizes the precession dynamics. For fixed individual masses and spin magnitudes, an equalmass black-hole inspiral is uniquely characterized by the two parameters (S, ξ): these two numbers completely determine the entire evolution under the effect of radiation reaction. In particular, for equal-mass binaries we find that (i) the black-hole binary spin morphology is constant throughout the inspiral, and that (ii) the precessional motion of the two black-hole spins about the total spin takes place on a longer timescale than the precession of the total spin and the orbital plane about the total angular momentum.
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