# 2015 CAP Congress / Congrès de l'ACP 2015

13-19 June 2015
University of Alberta
America/Edmonton timezone
Welcome to the 2015 CAP Congress! / Bienvenue au congrès de l'ACP 2015!

## Restricted Weyl Invariance in Four-Dimensional Curved Spacetime

17 Jun 2015, 09:15
15m
CAB 235 (University of Alberta)

### CAB 235

#### University of Alberta

Oral (Non-Student) / orale (non-étudiant) Theoretical Physics / Physique théorique (DTP-DPT)

### Speaker

Prof. Ariel Edery (Bishop's)

### Description

We discuss the physics of *restricted Weyl invariance*, a symmetry of dimensionless actions in four dimensional curved space time. When we study a scalar field nonminimally coupled to gravity with Weyl(conformal) weight of $-1$ (i.e. scalar field with the usual two-derivative kinetic term), we find that dimensionless terms are either fully Weyl invariant or are Weyl invariant if the conformal factor $\Omega(x)$ obeys the condition $g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}\Omega=0$. We refer to the latter as *restricted Weyl invariance*. We show that all the dimensionless geometric terms such as $R^2$, $R_{\mu\nu}R^{\mu\nu}$ and $R_{\mu\nu\sigma\tau}R^{\mu\nu\sigma\tau}$ are restricted Weyl invariant. Restricted Weyl transformations possesses nice mathematical properties such as the existence of a composition and an inverse in four dimensional space-time. We exemplify the distinction among rigid Weyl invariance, restricted Weyl invariance and the full Weyl invariance in dimensionless actions constructed out of scalar fields and vector fields with Weyl weight zero.

### Primary authors

Prof. Ariel Edery (Bishop's) Dr Yu Nakayama (Caltech)

 Slides