13ª Semana Integrada do Instituto de Física de São Carlos

The hidden symmetries of Yang-Mills theory on loop spaces

21 de ago. de 2023 10:30

1h 30m

Salão de Eventos USP

Prêmio YPM 10h30 - 12h00

Descrição

Even though the integral form of the equations of classical electrodynamics is well known, the same does not hold for non-abelian gauge theories. In 2012, L. A. Ferreira and G. Luchini, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem, presented an integral form of the classical Yang-Mills equations and used it to solve the long-standing problem of constructing non-abelian electric and magnetic conserved charges, for any field configurations, that are invariant under general gauge transformations. (1,2) In this poster, we present a novel symmetry of non-abelian gauge theories. It corresponds to an infinite symmetry group of the integral Yang-Mills equations, where the group elements are holonomies of connections on loop space. It differs from the usual holonomy group in the sense that its product law defines a composition of connections on every loop, and not a composition of loops. (3) In addition, the integral Yang-Mills equations are equivalent to a zero curvature condition for a connection on loop space, and that group constitutes the group of gauge transformations of those flat connections.

Referências

1 FERREIRA, L. A.; LUCHINI, G. Gauge and integrable theories in loop spaces. Nuclear Physics B, v. 858, n. 2, p. 336-365, May 2012.

2 FERREIRA, L. A.; LUCHINI, G. Integral form of Yang-Mills equations and its gauge invariant conserved charges. Physical Review D, v. 86, n. 8, p.085039-1-085039-22, Oct. 2012.

3 NAKAHARA, M. Geometry and topology and physics. 2nd ed. Boca Raton: CRC Press, 2003. 596 p. (Graduate Student Series in Physics).