Homotopy Algebras in Higher Spin Theory
arXiv:1807.06037 · doi:10.4310/ATMP.2020.v24.n3.a5
Abstract
Motivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation in terms of the Maurer-Cartan equation associated to differential forms valued in L-infinity algebras. The elimination of auxiliary variables of Vasiliev equation is analyzed through homological perturbation theory. This leads to a closed combinatorial graph formula for all the vertices of higher spin equations in the unfolded formulation. We also discover a topological quantum mechanics model whose correlation functions give deformed higher spin vertices at first order.
arXiv comment46 pages. Comments are welcome
References in corpus (25)
- Deformation quantization of Poisson manifolds, I
- AdS Dual of the Critical O(N) Vector Model
- Closed String Field Theory: Quantum Action and the BV Master Equation
- Introduction to string field theory
- Introduction to sh Lie algebras for physicists
- Higher Spin Gauge Theory and Holography: The Three-Point Functions
- Higher Spin Gauge Theories: Star-Product and AdS Space
- How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
- Lie theory for nilpotent L-infinity algebras
- On higher spins and the tensionless limit of String Theory
- The Higher Spin/Vector Model Duality
- Oriented Open-Closed String Theory Revisited
- On the Tensionless Limit of Bosonic Strings, Infinite Symmetries and Higher Spins
- Analysis of Higher Spin Field Equations in Four Dimensions
- Elements of Vasiliev theory
- On the perturbation lemma, and deformations
- Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
- Introduction to A-infinity algebras and modules
- Formal solution of the master equation via HPT and deformation theory
- Twisted supergravity and its quantization
- Holography and Koszul duality: the example of the brane
- Homotopy Operators and Locality Theorems in Higher-Spin Equations
- Batalin-Vilkovisky quantization and the algebraic index
- Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
- On Curvature Expansion of Higher Spin Gauge Theory