Functional renormalization group analysis of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> nonlinear

It is known that the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo></a:math> Wess-Zumino-Witten model is dual to the free fermion theory in two dimensions via non-Abelian bosonization. While it is decomposed into the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>2</e:mn><e:mo stretchy="false">)</e:mo></e:math> Wess-Zumino-Witten model and a free compact boson, the former is believed to be equivalent to the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>O</i:mi><i:mo stretchy="false">(</i:mo><i:mn>3</i:mn><i:mo stretchy="false">)</i:mo></i:math> nonlinear sigma model with the theta term at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>θ</m:mi><m:mo>=</m:mo><m:mi>π</m:mi></m:math>. In this work, we reexamine this duality through the lens of nonperturbative renormalization group (RG) flow. We analyze the RG flow structure of the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>O</o:mi><o:mo stretchy="false">(</o:mo><o:mn>3</o:mn><o:mo stretchy="false">)</o:mo></o:math> nonlinear sigma model with the theta term in two dimensions using the functional renormalization group. Our results reveal a nontrivial fixed point with a nonzero value of the topological coupling. The scaling dimensions (critical exponents) at this fixed point suggest the realization of a duality between the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>O</s:mi><s:mo stretchy="false">(</s:mo><s:mn>3</s:mn><s:mo stretchy="false">)</s:mo></s:math> nonlinear sigma model with the theta term and the free fermion theory, indicating that these models belong to the same universality class.