Anomalous dimensions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>ϕ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math> in scale invariant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:math> theory

Abstract

Recently it was shown that the scaling dimension of the operator ${\ensuremath{\phi}}^{n}$ in scale invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading $n$. Here we extend this verification to six loops, once again at leading and subleading $n$. We then perform a similar exercise for a theory with a multiplet of real scalars and an $O(N)$ invariant hexic interaction. We also investigate the strong-coupling regime for this example.

Topics & Concepts