The Coleman-Weinberg mechanism in a conformal (Weyl) invariant theory: application to a magnetic monopole

9th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Edery, Ariel^1 ; Graham, Noah^2

Department of Physics, Bishop's University, 2600 College Street, Sherbrooke

QC

J1M 1Z7, Canada^1

Department of Physics, Middlebury College, Middlebury

VT

05753, United States^2

关键词: Effective potentials;    Expectation values;    Invariant theory;    Magnetic monopoles;    Quantum correction;    Renormalization;    Scalar coupling;    Spontaneous symmetry breaking;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/615/1/012005/pdf
DOI  :  10.1088/1742-6596/615/1/012005

来源: IOP

【 摘 要 】

We consider a massless conformally (Weyl) invariant classical action consisting of a magnetic monopole coupled to gravity in an anti-de Sitter background spacetime. We implement quantum corrections and this breaks the conformal (Weyl) symmetry, introduces a length scale via the process of renormalization and leads to the trace anomaly. We calculate the one-loop effective potential and determine from it the vacuum expectation value (VEV). Spontaneous symmetry breaking is radiatively induced a la Coleman-Weinberg and the scalar coupling constant is exchanged for the dimensionful VEV via dimensional transmutation. An important result is that the Ricci scalar of the AdS background spacetimeis determined entirely by the value of the VEV.