Large- N solution and effective action of a twisted-mass deformed CP(N−1) model

We study effective dynamics of the nonsupersymmetric two-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mrow><a:mi mathvariant="double-struck">CP</a:mi></a:mrow><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo>−</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> model in the large <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>N</f:mi></f:math> limit. This model is deformed by a mass term <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>m</h:mi></h:math> preserving <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi mathvariant="double-struck">Z</j:mi><j:mi>N</j:mi></j:msub></j:math> symmetry of the Lagrangian. At small <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>m</m:mi></m:math> the theory is strongly coupled and resembles the undeformed <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mi mathvariant="double-struck">CP</o:mi></o:mrow><o:mo stretchy="false">(</o:mo><o:mi>N</o:mi><o:mo>−</o:mo><o:mn>1</o:mn><o:mo stretchy="false">)</o:mo></o:math> model, while at large <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>m</t:mi></t:math> it is in a weakly coupled Higgs phase with spontaneously broken <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msub><v:mi mathvariant="double-struck">Z</v:mi><v:mi>N</v:mi></v:msub></v:math>. We find the phase transition point and discuss the fate of the kink-antikink “mesons” at strong coupling. We also resolve an issue of instability that arose in previous studies of this model. Published by the American Physical Society 2024