Year: 2018
Type: article
Abstract: A general mechanism for the loss of conformal invariance is the merger and disappearance of an infrared fixed point and an ultraviolet fixed point of a renormalization group flow. We show explicitly how this mechanism works in the case of identical bosons at unitarity as the spatial dimension $d$ is varied. For $d$ between the critical dimensions ${d}_{1}=2.30$ and ${d}_{2}=3.76$, there is loss of conformality as evidenced by the Efimov effect in the three-body sector. The $\ensuremath{\beta}$ function for an appropriate three-body coupling is a quadratic polynomial in that coupling. For $d<{d}_{1}$ and for $d>{d}_{2}$, the $\ensuremath{\beta}$ function has two real roots that correspond to infrared and ultraviolet fixed points. As $d$ approaches ${d}_{1}$ from below and as $d$ approaches ${d}_{2}$ from above, the fixed points merge and disappear into the complex plane. For ${d}_{1}<d<{d}_{2}$, the $\ensuremath{\beta}$ function has complex roots and the renormalization group flow for the three-body coupling is a limit cycle.
Source: Physical Review A
Authors: Abhishek Mohapatra, Eric Braaten
Institution: The Ohio State University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2766765428