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# Advances in Theoretical and Mathematical Physics

## Volume 24 (2020)

### Number 3

### Homotopy algebras in higher spin theory

Pages: 757 – 819

DOI: https://dx.doi.org/10.4310/ATMP.2020.v24.n3.a5

#### Authors

#### 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 $L_\infty$-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.

Published 19 August 2020