Classical algebraic structures in string theory effective actions

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.

Tree-level S-matrix of superstring field theory with homotopy algebra structure

“…The relation(2.52) shows that the map i ≡ (Î − HLint) −1P (deformed inclusion map in the language of HPT) is a cohomomorphism. This was first shown in ref [39]. for the first couple of orders in Lint, and subsequently proven in ref [40]…”

“…He also would like to thank Jakub Vošmera for drawing his attention to refs. [39,40]. He also would like to express his appreciation to organizers of "Fundamental Aspects of String Theory" ICTP-SAIFR, Sao Paulo 1-12 June 2020, in particular Nathan Berkovits, for providing exciting atmosphere through the online workshop.…”

Closed string deformations in open string field theory. Part I. Bosonic string

“…Following [41,[63][64][65] there is interest in these days to explicitly address the computation of the effective couplings for the massless fields that one gets in string field theory by integrating out the massive excitations [66][67][68][69][70][71]. In particular very recently the systematic construction of effective open-closed couplings in bosonic Witten open string field theory has been carried out in [70,71]. In this and the companion papers [83,84] we continue in this direction and we will also extend the open-closed effective couplings in the context of open superstring field theory.…”

“…The paper is organized as follows. In section 2 we address the physical problem of removing the closed string tadpole by shifting the open string vacuum to a perturbative classical solution and we review the construction of the open-closed couplings in Witten OSFT as described in [70,71]. The possible obstructions to the existence of such a solution are precisely given by the equation of motion of the (closed-string deformed) effective action.…”

Gauge invariant perturbation theory via homotopy transfer

“…The L ∞ formulation is also closely related to the classical limit of the Batalin-Vilkovisky (BV) formulation of field theory [23,24]; more precisely, the tangent space to the BV manifold is the vector space of the L ∞ algebra, and the L ∞ brackets are recovered as the Taylor coefficients of the BV differential, which acts on the dual space of functions [25].) Homotopy transfer refers to a map from an L ∞ algebra to another, generally 'smaller' L ∞ algebra that is homotopy equivalent (see [22,26] for pedagogical introductions and [27][28][29]32] for recent applications). We will show that passing over to gauge invariant Bardeen-type variables can be interpreted as homotopy transfer.…”