PIRSA:19020035

SO(7,7) structure of the SM fermions

APA

Krasnov, K. (2019). SO(7,7) structure of the SM fermions. Perimeter Institute. https://pirsa.org/19020035

MLA

Krasnov, Kirill. SO(7,7) structure of the SM fermions. Perimeter Institute, Feb. 28, 2019, https://pirsa.org/19020035

BibTex

          @misc{ pirsa_19020035,
            doi = {10.48660/19020035},
            url = {https://pirsa.org/19020035},
            author = {Krasnov, Kirill},
            keywords = {Quantum Gravity},
            language = {en},
            title = {SO(7,7) structure of the SM fermions},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020035 see, \url{https://pirsa.org}}
          }
          

Kirill Krasnov University of Nottingham

Collection
Talk Type Scientific Series
Subject

Abstract

I will describe the relevant representation theory that allows to think of all components of fermions of a single generation of the Standard Model as components of a single Weyl spinor of an orthogonal group whose complexification is SO(14,C). There are then only two real forms that do not lead to fermion doubling. One of these real forms is the split signature orthogonal group SO(7,7). I will describe some exceptional phenomena that occur for the orthogonal groups in 14 dimensions, and then specifically for this real form. The real form SO(7,7) suggests a link to generalised geometry, which I will describe. I will also describe why spinors in general are really differential forms in disguise.