Nonperturbative features in the Lie-algebraic K\"ahler sigma model with fermions

We investigate the trans-series structure of a quantum mechanical system originating from a Lie-algebraic K\"ahler sigma model with multiple right-handed chiral fermions, extending previous results for the standard onecomplex projective ($\mathbb{CP}^1$) model [1],[2] 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 $\mathbb{CP}^1$ 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.