Revisiting the ϕ6 theory in three dimensions at large N

We investigate the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>O</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:math>-symmetric <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>ϕ</e:mi><e:mn>6</e:mn></e:msup></e:math> theory in three spacetime dimensions using dimensional regularization and minimal subtraction. The predictions of other methods are scrutinized in a large-<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>N</g:mi></g:math> expansion. We show how the tricritical line of fixed point emerges in a strict <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>N</i:mi><i:mo stretchy="false">→</i:mo><i:mi>∞</i:mi></i:math> limit but argue that it is not a physical manifestation. For the first time in this explicit manner, we compute the effective potential at next-to-leading order in the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mn>1</l:mn><l:mo>/</l:mo><l:mi>N</l:mi></l:math>-expansion and discuss its stability. The Bardeen-Moshe-Bander phenomenon is also analysed at next-to-leading order, and we demonstrate that it disappears without breaking the scale invariance spontaneously. Our findings indicate that the UV fixed point found by Pisarski persists at large <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>N</n:mi></n:math>.