On operad structures of moduli spaces and string theory

Abstract

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.

33 pages (An elaboration of minimal area metrics and new references are added)

References in corpus (12)

• Closed String Field Theory: Quantum Action and the BV Master Equation
• Introduction to string field theory
• Introduction to sh Lie algebras for physicists
• Operads, homotopy algebra and iterated integrals for double loop spaces
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Semiclassical approximation in Batalin-Vilkovisky formalism
• New Perspectives on the BRST-algebraic Structure of String Theory
• Two-dimensional topological gravity and equivariant cohomology
• Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli space
• Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras
• Chow quotients of Grassmannian I
• On Some Algebraic Structures Arising in String Theory

Cited by in corpus (62)

• Homotopy G-algebras and moduli space operad
• Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings
• Noncommutative homotopy algebras associated with open strings
• Topological Open P-Branes
• Homotopy algebras inspired by classical open-closed string field theory
• The Dilaton Theorem and Closed String Backgrounds
• BV Quantization of Topological Open Membranes
• Bounds on spectral norms and barcodes
• Symplectic cohomology and q-intersection numbers
• BCOV theory via Givental group action on cohomological field theories
• Open-closed homotopy algebra in mathematical physics
• A Note on Gauge Transformations in Batalin-Vilkovisky Theory
• On the Open-Closed B-Model
• Topological Open Membranes
• Deformations of Closed Strings and Topological Open Membranes
• Les Houches Lectures on Fields, Strings and Duality
• Homotopy Algebras for Operads
• Symplectic and contact differential graded algebras
• Topological conformal field theories and Calabi-Yau categories
• The Gromov-Witten potential associated to a TCFT
• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory
• Toric varieties of Loday's associahedra and noncommutative cohomological field theories
• A Diagonal on the Associahedra
• Disjoinable Lagrangian spheres and dilations
• Construction of a Gauge-Invariant Action for Type II Superstring Field Theory
• Homotopy Gerstenhaber algebras and topological field theory
• N=2 structures in all string theories
• Tautological relations in Hodge field theory
• A functional-analytic theory of vertex (operator) algebras, I
• Super, quantum and non-commutative species
• Topological field theories, string backgrounds and homotopy algebras
• Homotopy algebra of open-closed strings
• r${}_{\infty }$-Matrices, triangular L${}_{\infty }$-bialgebras, and quantum${}_{\infty }$ groups
• Hypercommutative operad as a homotopy quotient of BV
• Higher cyclic operads
• Gerstenhaber algebras and BV-algebras in Poisson geometry
• The geometry of Brownian surfaces
• Formal groups and quantum cohomology
• Deformation theory of Cohomological Field Theories
• Floer cohomology of $\mathfrak{g}$-equivariant Lagrangian branes
• New Moduli Spaces from String Background Independence Consistency Conditions
• From operads and PROPs to Feynman Processes
• The odd origin of Gerstenhaber brackets, Batalin-Vilkovisky operators, and master equations
• Infinite Dimensional Geometry and Quantum Field Theory of Strings. II. Infinite Dimensional Noncommutative Geometry of a Self-Interacting String Field
• Deformation Theory of Infinity Algebras
• Cyclic operad formality for compactified moduli spaces of genus zero surfaces
• Moduli of framed formal curves
• Some comments on the local curve (B-side)
• The quantum Johnson homomorphism and symplectomorphism of 3-folds
• Commutative Quantum Operator Algebras
• Untwisting Topological Field Theories
• Open-closed moduli spaces and related algebraic structures
• Operads for x-physics
• BV-generators and Lie algebroids
• Batalin--Vilkovisky algebra structures on the Hochschild cohomology of generalized Weyl algebras
• Formality of little disks and algebraic geometry
• On the BV structure on the cohomology of moduli space
• Hyper-commutative algebras and cyclic cohomology
• The Bagger-Lambert model and Type IIA string theory
• Semi-infinite forms and topological vertex operator algebras
• The Biderivative and A_\infty-bialgebras