The beta function of the vacuum energy density is analytically computed at the five-loop level in $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$-symmetric ${\phi }^4$ theory, using dimensional regularization in conjunction with the $\overline{\mathrm{MS}}$ scheme. The result for the case of cubic anisotropy is also given. It is pointed out how to also obtain the beta function of the coupling and the gamma function of the mass from vacuum graphs. This method may be easier than traditional approaches.

• Received 17 October 1997

DOI:https://doi.org/10.1103/PhysRevD.57.3567