Homotopy algebras, symplectic embeddings and non-commutative Gauge Theory

• Grant number: 21/09313-8
• Support Opportunities: Regular Research Grants
• Start date: December 01, 2021
• End date: November 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Vladislav Kupriyanov
• Grantee: Vladislav Kupriyanov
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Associated researchers: Richard J. Szabo

Abstract

The problem of the consistent definition of non-commutative gauge theory on spaces with non-constant non-commutativity parameter attracts attention of theoretical physicists and mathematicians for more than two decades. Nevertheless, this theory is still not completely understood in full generality. In recent years in collaboration with the colleagues from Munich and Edinburgh we have formulated two new approaches to consistent non-commutative and non-associative deformations of gauge theory. The first one employs the framework of homotopy algebras and is a powerful tool for the construction of order by order non-commutative deformation. The second approach makes use of the elements from the symplectic geometry and is better adapted for obtaining of the explicit all-order expressions. Several interesting results have been obtained and published in this direction. In this project, we briefly describe the two approaches and formulate the topics of the future research, including the further development of the mathematical formalism and its application to the investigation of physical effects caused by the non-commutativity. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

KUPRIYANOV, VLADISLAV G.; SZABO, RICHARD J.. Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry. Journal of Physics A-Mathematical and Theoretical, v. 55, n. 3, JAN 21 2022. (21/09313-8)

ABLA, O.; KUPRIYANOV, V. G.; KURKOV, M. A.. On the L-infinity structure of Poisson gauge theory. Journal of Physics A-Mathematical and Theoretical, v. 55, n. 38, p. 32-pg., 2022-09-23. (21/09313-8)

KUPRIYANOV, V. G.; KURKOV, M. A.; VITALE, P.. Poisson gauge models and Seiberg-Witten map. Journal of High Energy Physics, v. N/A, n. 11, p. 27-pg., 2022-11-11. (21/09313-8)