Homotopy algebras inspired by classical open-closed string field theory

Abstract

We define a homotopy algebra associated to classical open-closed strings. We call it an open-closed homotopy algebra (OCHA). It is inspired by Zwiebach's open-closed string field theory and also is related to the situation of Kontsevich's deformation quantization. We show that it is actually a homotopy invariant notion; for instance, the minimal model theorem holds. Also, we show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A(infinity)-algebras) by closed strings (L(infinity)-algebras).

30 pages, 14 figures; v2: added an appendix by M.Markl, ambiguous terminology fixed, minor corrections; v3: published version

References in corpus (18)

• Deformation quantization of Poisson manifolds, I
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Introduction to string field theory
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Introduction to sh Lie algebras for physicists
• A path integral approach to the Kontsevich quantization formula
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• Oriented Open-Closed String Theory Revisited
• Tensor Constructions of Open String Theories I: Foundations
• On operad structures of moduli spaces and string theory
• Cohomology and Deformation of Leibniz Pairs
• Homotopy Algebra Morphism and Geometry of Classical String Field Theory
• Formal solution of the master equation via HPT and deformation theory
• Classical Open-String Field Theory ; $A_{\infty }$-Algebra, Renormalization Group and Boundary States
• Open-closed homotopy algebra in mathematical physics
• On the Open-Closed B-Model
• Deformations of Topological Open Strings

Cited by in corpus (29)

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• Quantum Open-Closed Homotopy Algebra and String Field Theory
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• The classical cosmological constant of open-closed string field theory
• Lie 2-algebra models
• Actions of monoidal categories and representations of Cartan type Lie algebras
• Homotopy algebra of open-closed strings
• Double field theory algebroid and curved $L_{\infty }$-algebras
• The Hochschild Complex of a Finite Tensor Category
• Swiss-Cheese operad and Drinfeld center
• On deformations of $A_{\infty }$-algebras
• Floer cohomology of $\mathfrak{g}$-equivariant Lagrangian branes
• HS in flat spacetime. The effective action method
• On the Spectral Sequence of the Swiss-cheese Operad
• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• The modular class of a singular foliation
• Relative Recognition Principle
• On the $L_{\infty }$ formulation of Chern-Simons theories
• Invariants from classical field theory
• Algebraic Structures In Closed Superstring Field Theory, Homotopy Transfer And Effective Actions
• Calculus of multilinear differential operators, operator $L_{\infty }$-algebras and ${IBL}_{\infty }$-algebras
• On open-closed extension of boundary string field theory
• An Algebraic Model for the su(2|2) Light-Cone String Field Theory
• Type II superstring field theory revisited
• Homotopy representations of extended holomorphic symmetry in holomorphic twists
• Bulk deformations of open topological string theory
• Closed string amplitudes around tachyon vacuum solution in Kaku theory
• Stability and rigidity of 3-Lie algebra morphisms