Noncommutative Gauge Dynamics from L_infinity- Algebras

• Grant number: 24/23831-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2025
• End date: February 29, 2028
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Vladislav Kupriyanov
• Grantee: Eduardo Lourenço Fabio de Lima
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

Non-commutative (NC) gauge theories on coordinate-dependent space-time provide a robust framework to investigate deviations from classical physics, particularly when the non-commutativity parameter $\Theta^{ab}(x)$ varies with space-time coordinates. Using the $L_\infty$-algebra formalism, these theories encode higher-order corrections and ensure consistency through generalized Jacobi identities. This project extends the graded vector space $V = V_0 \oplus V_1$ to include $V_2$, the field strength tensor $\mathcal{F}_{\mu\nu}$ is incorporated, capturing the dynamical content of NC gauge theories. The $L_\infty$-bootstrap method systematically constructs these deformations, maintains gauge covariance, and ensures algebraic closure. This unified formalism provides a powerful tool to explore the algebraic, geometric, and physical implications of NC gauge theories.