Homotopy Algebra Morphism and Geometry of Classical String Field Theory

Abstract

We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background there are many string field theories corresponding to different decomposition of moduli space of Riemann surfaces. It is shown that any classical open string field theories on a fixed conformal background are $A_{\infty }$-quasi-isomorphic to each other. This indicates that they have isomorphic moduli space of classical solutions. The minimal model theorem in $A_{\infty }$-algebras plays a key role in these results. Its natural and geometric realization on formal supermanifolds is also given. The same results hold for classical closed string field theories, whose algebraic structure is governed by $L_{\infty }$-algebras.

79 pages, the first half is based on the review talk presented at the Summer Institute 2001 at Fuji-Yoshida in Japan, v2: figures and typos corrected

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Cited by in corpus (37)

• Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Noncommutative homotopy algebras associated with open strings
• Chern-Simons Gauge Theory coupled with BF Theory
• Double Copy from Homotopy Algebras
• Homotopy algebras inspired by classical open-closed string field theory
• NS-NS Sector of Closed Superstring Field Theory
• Scattering Amplitude Recursion Relations in BV Quantisable Theories
• D-brane categories
• D-instantons, String Field Theory and Two Dimensional String Theory
• Quantum Open-Closed Homotopy Algebra and String Field Theory
• Classical algebraic structures in string theory effective actions
• Loop Amplitudes and Quantum Homotopy Algebras
• Mapping between Witten and Lightcone String Field Theories
• Closed String Cohomology in Open String Field Theory
• Cutkosky Rules and Unitarity (Violation) in D-instanton Amplitudes
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Open string stub as an auxiliary string field
• $L_{\infty }$-Algebras of Einstein-Cartan-Palatini Gravity
• Construction of a Gauge-Invariant Action for Type II Superstring Field Theory
• Quantum A-infinity Structures for Open-Closed Topological Strings
• Closed string deformations in open string field theory II: superstring
• Homotopy algebra of open-closed strings
• Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
• Closed string deformations in open string field theory I: bosonic string
• Homological mirror symmetry on noncommutative two-tori
• Light-cone reduction of Witten's open string field theory
• Homotopy Classification of Bosonic String Field Theory
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras
• Poisson Sigma Model with branes and hyperelliptic Riemann surfaces
• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• Algebraic Structures In Closed Superstring Field Theory, Homotopy Transfer And Effective Actions
• Generalised wavefunction coefficients and acyclonesto-cosmohedra
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• On the BV formalism of open superstring field theory in the large Hilbert space
• The $L_{\infty }$-algebra of the S-matrix
• An $A_{\infty }$-structure for lines in a plane