The Higher Algebra of Supersymmetry


Huerta, J. (2021). The Higher Algebra of Supersymmetry. Perimeter Institute. https://pirsa.org/21030015


Huerta, John. The Higher Algebra of Supersymmetry. Perimeter Institute, Mar. 29, 2021, https://pirsa.org/21030015


          @misc{ pirsa_PIRSA:21030015,
            doi = {10.48660/21030015},
            url = {https://pirsa.org/21030015},
            author = {Huerta, John},
            keywords = {Mathematical physics, Particle Physics, Quantum Fields and Strings},
            language = {en},
            title = {The Higher Algebra of Supersymmetry},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {mar},
            note = {PIRSA:21030015 see, \url{https://pirsa.org}}

John Huerta University of Lisbon


We have already met the octonionic Fierz identity satisfied by spinors in 10-dimensional spacetime. This identity makes super-Yang-Mills "super" and allows the Green-Schwarz string to be kappa symmetric. But it is also the defining equation of a "higher" algebraic structure: an L-infinity algebra extending the supersymmetry algebra. We introduce this L-infinity algebra in octonionic language, and describe its cousins in various dimensions. We then survey various consequences of its existence, such as the brane bouquet of Fiorenza-Sati-Schreiber.