Homotopy transfer for conserved currents and rigid symmetries in gauge theories

Igor Khavkine (IM CAS)

Sep 07. 2021, 14:00 — 15:00

In Lagrangian field theory, Noether's theorem connects symmetries and conserved currents (on-shell closed local forms in degree $n-1$). The BV formalism allows to extend this connection to "higher" symmetries and conserved currents in lower form degrees, via BRST cohomology in field-antifield dependent local forms. I will describe how, within this framework, the theory of higher algebraic structures explains the appearance of seldom noticed $L_\infty$ and $C_\infty$ structures stemming from the Lie algebra of infinitesimal symmetries and the graded commutative algebra of differential forms. This is a report on work in progress.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and Q-manifolds (Thematic Programme)
Xavier Bekaert (U of Tours)
Andreas Cap (U of Vienna)
Stefan Fredenhagen (U of Vienna)
Maxim Grigoriev (U of Mons)
Alexei Kotov (U Hradec Králové)