Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions

We investigate the trans-series structure of a quantum mechanical system originating from a Lie-algebraic Kähler sigma model with multiple right-handed chiral fermions, extending previous results for the standard one-dimensional complex projective (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi mathvariant="double-struck">CP</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msup></a:mrow></a:math>) model [T. Fujimori , Nonperturbative contributions from complexified solutions in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="double-struck">C</d:mi><d:msup><d:mi>P</d:mi><d:mrow><d:mi>N</d:mi><d:mo>−</d:mo><d:mn>1</d:mn></d:mrow></d:msup></d:math> models, ; T. Fujimori Exact resurgent trans-series and multibion contributions to all orders, ] to its deformed counterpart. We identify and analyze saddle-point solutions and examine their contributions within the perturbative expansions of the ground-state energy, revealing that the ambiguity structure observed in the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mrow><g:mi mathvariant="double-struck">CP</g:mi></g:mrow><g:mn>1</g:mn></g:msup></g:math> model persists in the deformed model as well. Additionally, we explore the role of the elongation parameter and its potential impact on higher-loop corrections and propose that it becomes relevant in shaping the system’s quantum behavior from the three-loop level. This verifies that the trans-series framework provides a comprehensive approach to capturing the structure of quantum fluctuations and ambiguities in these deformed sigma models.