Year: 2017
Type: article
Abstract: The renormalization group functions for six dimensional scalar ${\ensuremath{\phi}}^{3}$ theory with an ${F}_{4}$ symmetry are provided at four loops in the modified minimal subtraction ($\overline{\mathrm{MS}}$) scheme. Aside from the anomalous dimension of $\ensuremath{\phi}$ and the $\ensuremath{\beta}$-function this includes the mass operator and a ${\ensuremath{\phi}}^{2}$-type operator. The anomalous dimension of the latter is computed explicitly at four loops for the $\mathbf{26}$ and $\mathbf{324}$ representations of ${F}_{4}$. The $\ensuremath{\epsilon}$ expansion of all the related critical exponents are determined to $O({\ensuremath{\epsilon}}^{4})$. For instance the value for ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\phi}}$ agrees with recent conformal bootstrap estimates in 5 and 5.95 dimensions. The renormalization group functions are also provided at four loops for the group ${E}_{6}$.
Author: J. A. Gracey
Institution: University of Liverpool
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2595573699