Heavy handed quest for fixed points in multiple coupling scalar theories in the ε expansion

The tensorial equations for non trivial fully interacting fixed points at lowest order in the epsilon expansion in 4 - epsilon and 3 - epsilon dimensions are analysed for N-component fields and corresponding multi-index couplings lambda which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For N = 5, 6, 7 in the four-index case large numbers of irrational fixed points are found numerically where lambda (2) is close to the bound found by Rychkov and Stergiou [1]. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For N 6 the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for N = 5.

Automated summary

The tensorial equations for non trivial fully interacting fixed points are analyzed for N-component fields with symmetric tensor couplings. Large numbers of irrational fixed points are found numerically, but no solutions saturating the bound are discovered. These examples generally lack unique quadratic invariants in the fields.