2017/06/27 by Blumenhagen, Ralph, Fuchs, Michael, Traube, Matthias
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1706.09034
It is believed that any classical gauge symmetry gives rise to an L_∞ algebra. Based on the recently realized relation between classical \cal W algebras and L_∞ algebras, we analyze how this generalizes to the quantum case. Guided by the existence of quantum \cal W algebras, we provide a physically well motivated definition of quantum L_∞ algebras describing the consistency of global symmetries in quantum field theories. In this case we are restricted to only two non-trivial graded vector spaces X0 and X-1 containing the symmetry variations and the symmetry generators. This quantum L_∞ algebra structure is explicitly exemplified for the quantum \cal W3 algebra. The natural quantum product between fields is the normal ordered one so that, due to contractions between quantum fields, the higher L_∞ relations receive off-diagonal quantum corrections. Curiously, these are not present in the loop L_∞ algebra of closed string field theory.