Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification

We investigate the thermodynamics and phase structure of <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:mn>3</a:mn><a:mo stretchy="false">)</a:mo></a:math> Yang-Mills theory on <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi mathvariant="double-struck">T</e:mi><e:mn>2</e:mn></e:msup><e:mo>×</e:mo><e:msup><e:mi mathvariant="double-struck">R</e:mi><e:mn>2</e:mn></e:msup></e:math> in Euclidean spacetime in an effective-model approach. The model incorporates two Polyakov loops along two compactified directions as dynamical variables, and is constructed to reproduce thermodynamics on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi mathvariant="double-struck">T</i:mi><i:mn>2</i:mn></i:msup><i:mo>×</i:mo><i:msup><i:mi mathvariant="double-struck">R</i:mi><i:mn>2</i:mn></i:msup></i:math> measured on the lattice. The model analysis indicates the existence of a novel first-order phase transition on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi mathvariant="double-struck">T</m:mi><m:mn>2</m:mn></m:msup><m:mo>×</m:mo><m:msup><m:mi mathvariant="double-struck">R</m:mi><m:mn>2</m:mn></m:msup></m:math> in the deconfined phase, which terminates at critical points that should belong to the two-dimensional <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>Z</q:mi><q:mn>2</q:mn></q:msub></q:math> universality class. We argue that the interplay of the Polyakov loops induced by their cross-term in the Polyakov-loop potential is responsible for the manifestation of the first-order transition. Published by the American Physical Society 2024