Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops

We renormalize the Gross-Neveu-Yukawa model with an <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> symmetry to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi mathvariant="script">O</e:mi> <e:mo stretchy="false">(</e:mo> <e:msup> <e:mi>ε</e:mi> <e:mn>5</e:mn> </e:msup> <e:mo stretchy="false">)</e:mo> </e:math> in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>d</j:mi> <j:mo>=</j:mo> <j:mn>4</j:mn> <j:mo>−</j:mo> <j:mi>ε</j:mi> </j:math> dimensions and determine the anomalous dimensions of the fermion and scalar fields, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>β</l:mi> </l:math> functions as well as the scalar field’s mass operator. These are used to construct several <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>N</n:mi> </n:math> -dependent critical exponents relevant for quantum transitions in semimetals and in particular those connected with graphene in three dimensions when <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>N</p:mi> <p:mo>=</p:mo> <p:mn>2</p:mn> </p:math> . Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>N</r:mi> <r:mo>=</r:mo> <r:mn>1</r:mn> </r:math> , as well as for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>N</t:mi> <t:mo>=</t:mo> <t:mn>5</t:mn> </t:math> are also given to compare with results from other techniques such as the conformal bootstrap.