Lie algebroids, Koszul duality, pure spinor formalism

• Grant number: 25/00641-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2025
• End date: March 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Andrey Yuryevich Mikhaylov
• Grantee: Diana Cruz Pestana
• Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
• Associated research grant: 21/14335-0 - ICTP South American Institute for Fundamental Research: a regional center for Theoretical Physics, AP.ESP

Abstract

Lie algebroids are objects that arise naturally in several areas of mathematics and physics. They are a natural generalization of Lie algebras, conceptually related to gauge field theories. In particular, there is an elegant mathematical construction of Free Lie Algebroids. Quadratic Lie superalgebras play an important role in the pure spinor description of Yang-Mills theory via Koszul duality. It has been conjectured that quadratic-linear Lie algebroids may play an analogous role in supergravity. However, it seems that the related mathematical concepts are relatively new and have not been sufficiently developed. We propose to study the quadratic-linear Koszul duality for algebroids, and investigate its possible relation to pure spinor formalism and supergravity. (AU)