Event Details

I will review L-infinity (or strongly homotopy Lie) algebras and their relation to field theories in theoretical physics. L-infinity algebras are generalizations of Lie algebras in which the Jacobi identity may be violated, in a way that is controlled by `higher’ brackets. These algebras govern the gauge structure of closed string field theory, but are not usually thought of as playing a role in conventional field theories. I will argue that, on the contrary, field theories are in one-to-one correspondence with L-infinity algebras, with the gauge algebra, interactions, etc. of a field theory being encoded in the higher brackets of an L-infinity algebra. I will discuss double field theory and possible generalizations as examples.