Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry

Author(s)

Kupriyanov, Vladislav G. ^{[1, 2]} ; Szabo, Richard J. ^{[3, 4, 5]}

Affiliation

^[1] Tomsk State Univ, Tomsk - Russia

^[2] Univ Fed ABC, Ctr Matemat Computacao & Cognicao, Santo Andre, SP - Brazil

^[3] Heriot Watt Univ, Dept Math, Colin Maclaurin Bldg, Riccarton, Edinburgh EH14 4AS, Midlothian - Scotland

^[4] Maxwell Inst Math Sci, Edinburgh, Midlothian - Scotland

^[5] Higgs Ctr Theoret Phys, Edinburgh, Midlothian - Scotland

• Document type: Journal article
• Source: Journal of Physics A-Mathematical and Theoretical; v. 55, n. 3 JAN 21 2022.
• Web of Science Citations: 0

Abstract

We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by a P (infinity)-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by an L (infinity)-algebra which is not a P (infinity)-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define a P (infinity)-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based on A (infinity)-algebras. (AU)

• FAPESP's process: 21/09313-8 - Homotopy algebras, symplectic embeddings and non-commutative Gauge Theory
• Grantee: Vladislav Kupriyanov
• Support Opportunities: Regular Research Grants