Jun 13 – 19, 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

Jun 17, 2015, 9:15 AM
CAB 235 (University of Alberta)

CAB 235

University of Alberta

Oral (Non-Student) / orale (non-étudiant) Theoretical Physics / Physique théorique (DTP-DPT) W1-4 Gravity I (DTP) / Gravité I (DPT)


Prof. Ariel Edery (Bishop's)


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)

Presentation materials