# Anomaly-free special Weyl symmetry and particle physics

### APA

Shaposhnikov, M. (2022). Anomaly-free special Weyl symmetry and particle physics. Perimeter Institute. https://pirsa.org/22020060

### MLA

Shaposhnikov, Mikhail. Anomaly-free special Weyl symmetry and particle physics. Perimeter Institute, Feb. 16, 2022, https://pirsa.org/22020060

### BibTex

@misc{ pirsa_PIRSA:22020060, doi = {10.48660/22020060}, url = {https://pirsa.org/22020060}, author = {Shaposhnikov, Mikhail}, keywords = {Other}, language = {en}, title = {Anomaly-free special Weyl symmetry and particle physics}, publisher = {Perimeter Institute}, year = {2022}, month = {feb}, note = {PIRSA:22020060 see, \url{https://pirsa.org}} }

Mikhail Shaposhnikov L'Ecole Polytechnique Federale de Lausanne (EPFL)

## Abstract

What is the global symmetry of Nature? In the absence of gravity, the most obvious answer to this question is given by special relativity and is associated with the Poincare transformations. As was noted a long time ago, the free Maxwell equations have a wider symmetry group - the 15 parameters conformal invariance, containing in addition to ten Poincare generators, four special conformal transformations, and dilatations. Dilatations change the length of the rulers, while special conformal transformation can bend the lines but do not alter the angles between them. Could it be that the symmetry of all interactions is conformal? We will show that the answer to this question is "yes". The essential feature of the theory is the anomaly-free extension of the spontaneously broken conformal symmetry to curved space-time. We discuss how the effective Lagrangian respecting this special Weyl symmetry can be used for the description of particle phenomenology and cosmology.