Topological Open Membranes

Abstract

We study topological open membranes of BF type in a manifest BV formalism. Our main interest is the effect of the bulk deformations on the algebra of boundary operators. This forms a homotopy Lie algebra, which can be understood in terms of a closed string field theory. The simplest models are associated to quasi-Lie bialgebras and are of Chern-Simons type. More generally, the induced structure is a Courant algebroid, or ``quasi-Lie bialgebroid'', with boundary conditions related to Dirac bundles. A canonical example is the topological open membrane coupling to a closed 3-form, modeling the deformation of strings by a C-field. The Courant algebroid for this model describes a modification of deformation quantization. We propose our models as a tool to find a formal solution to the quantization problem of Courant algebroids.

40 pages

References in corpus (42)

• Dirichlet-Branes and Ramond-Ramond Charges
• Deformation quantization of Poisson manifolds, I
• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• The Geometry of the Master Equation and Topological Quantum Field Theory
• D-branes and Deformation Quantization
• Operads and Motives in Deformation Quantization
• D-branes from M-branes
• Some Comments On String Dynamics
• On Background Independent Open-String Field Theory
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Courant algebroids, derived brackets and even symplectic supermanifolds
• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• Algebraic Structures and Differential Geometry in 2D String Theory
• On the structure of open-closed topological field theory in two dimensions
• Duality Relations Among Topological Effects In String Theory
• On operad structures of moduli spaces and string theory
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• A Noncommutative M-Theory Five-brane
• Chern-Simons Gauge Theory As A String Theory
• Quantum Background Independence of Closed String Field Theory
• Balanced Topological Field Theories
• Duality and Non-Commutative Gauge Theory
• Topological Open P-Branes
• The Topological G/G WZW Model in the Generalized Momentum Representation
• Some Comments on Branes, G-flux, and K-theory
• Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops
• Open membranes in a constant C-field background and noncommutative boundary strings
• Theory of Kähler Gravity
• BV Quantization of Topological Open Membranes
• Deformation independent open brane metrics and generalized theta parameters
• Deformations of Batalin-Vilkovisky algebras
• The Master Equation of 2D String Theory
• Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli space
• On the Open-Closed B-Model
• General quantum antibrackets
• Comments on the topological open membrane
• Deformation complex of a d-algebra is a (d+1)-algebra
• Manin triples and $N=2$ superconformal field theory
• On Open/Closed String Duality
• Quantum observables, Lie algebra homology and TQFT

Cited by in corpus (11)

• Non-geometric Backgrounds and the First Order String Sigma Model
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• Lectures on AKSZ Sigma Models for Physicists
• BV Quantization of Topological Open Membranes
• Super-Chern-Simons Theory as Superstring Theory
• Lie 2-algebra models
• Nonassociative geometry and twist deformations in non-geometric string theory
• Deformation of Batalin-Vilkovisky Structures
• Topological B-model and $\hat{c}=1$ String Theory
• Flat family of QFTs and quantization of d-algebras
• An M-theory solution generating technique and SL(2,R)