Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\varepsilon$ Expansion

Understand

Fixed points for scalar theories in $4-\varepsilon$, $6-\varepsilon$ and $3-\varepsilon$ dimensions are discussed.

• It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings.
• The original maximal symmetry, $O(N)$, is broken to various subgroups, both discrete and continuous.
• A similar discussion is applied to the six dimensional case.