# Hidden patterns in the standard model of particle physics: the geometry of SO(10) unification

### APA

Krasnov, K. (2023). Hidden patterns in the standard model of particle physics: the geometry of SO(10) unification. Perimeter Institute. https://pirsa.org/23040160

### MLA

Krasnov, Kirill. Hidden patterns in the standard model of particle physics: the geometry of SO(10) unification. Perimeter Institute, Apr. 26, 2023, https://pirsa.org/23040160

### BibTex

@misc{ pirsa_PIRSA:23040160, doi = {10.48660/23040160}, url = {https://pirsa.org/23040160}, author = {Krasnov, Kirill}, keywords = {Other}, language = {en}, title = {Hidden patterns in the standard model of particle physics: the geometry of SO(10) unification}, publisher = {Perimeter Institute}, year = {2023}, month = {apr}, note = {PIRSA:23040160 see, \url{https://pirsa.org}} }

Kirill Krasnov University of Nottingham

## Abstract

The aim of the presentation is to review the beautiful geometry underlying the standard model of particle physics, as captured by the framework of "SO(10) grand unification." Some new observations related to how the Standard Model (SM) gauge group sits inside SO(10) will also be described.

I will start by reviewing the SM fermion content, organising the description in terms of 2-component spinors, which give the cleanest picture.

I will then explain a simple and concrete way to understand how spinors work in 2n dimensions, based on the algebra of differential forms in n dimensions.

This will be followed by an explanation of how a single generation of standard model fermions (including the right-handed neutrino) is perfectly described by a spinor in a 10 ("internal") dimensions.

I will review how the two other most famous "unification" groups -- the SU(5) of Georgi-Glashow and the SO(6)xSO(4) of Pati-Salam -- sit inside SO(10), and how the SM symmetry group arises as the intersection of these two groups, when they are suitably aligned.

I will end by explaining the more recent observation that the choice of this alignment, and thus the choice of the SM symmetry group inside SO(10), is basically the choice of two Georgi-Glashow SU(5) such that the associated complex structures in R^{10} commute. This means that the SM gauge group arises from SO(10) once a "bihermitian" geometry in R^{10} is chosen. I will end with speculations as to what this geometric picture may be pointing to.

Zoom link: https://pitp.zoom.us/j/95984379422?pwd=SE1ybktzQzcreWREblhEUkZWWElMUT09