Order of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>×</mml:mo><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math> chiral transition via the functional renormalization group

Abstract

Renormalization group flows of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:msub><a:mi>N</a:mi><a:mi>f</a:mi></a:msub><a:mo stretchy="false">)</a:mo><a:mo>×</a:mo><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:msub><a:mi>N</a:mi><a:mi>f</a:mi></a:msub><a:mo stretchy="false">)</a:mo></a:math> symmetric Ginzburg-Landau potential are calculated for a general number of flavors, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>N</g:mi><g:mi>f</g:mi></g:msub></g:math>. Our approach does not rely on the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>ε</i:mi></i:math> expansion, but uses the functional renormalization group, formulated directly in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>d</k:mi><k:mo>=</k:mo><k:mn>3</k:mn></k:math> spatial dimensions, with the inclusion of all possible (perturbatively) relevant and marginal operators, whose number is considerably larger than those in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>d</m:mi><m:mo>=</m:mo><m:mn>4</m:mn></m:math>. We find new, potentially infrared stable fixed points spanned throughout the entire <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>N</o:mi><o:mi>f</o:mi></o:msub></o:math> range. By conjecturing that the thermal chiral transition is governed by these “flavor continuous” fixed points, stability analyses show that for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>N</q:mi><q:mi>f</q:mi></q:msub><q:mo>≥</q:mo><q:mn>5</q:mn></q:math> the chiral transition is of second order, while for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>N</s:mi><s:mi>f</s:mi></s:msub><s:mo>=</s:mo><s:mn>2</s:mn></s:math>, 3, 4, it is of first order. We argue that the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>U</u:mi><u:mi mathvariant="normal">A</u:mi></u:msub><u:mo stretchy="false">(</u:mo><u:mn>1</u:mn><u:mo stretchy="false">)</u:mo></u:math> anomaly controls the strength of the first-order chiral transition for <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi>N</z:mi><z:mi>f</z:mi></z:msub><z:mo>=</z:mo><z:mn>2</z:mn></z:math>, 3, 4, and makes it almost indistinguishable from a second-order one, if it is sufficiently weak at the critical point. This could open up a new strategy to investigate the strength of the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>U</bb:mi><bb:mi mathvariant="normal">A</bb:mi></bb:msub><bb:mo stretchy="false">(</bb:mo><bb:mn>1</bb:mn><bb:mo stretchy="false">)</bb:mo></bb:math> symmetry breaking around the critical temperature. Published by the American Physical Society 2024

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