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

TL;DR

This paper explores the nonperturbative trans-series structure of a Lie-algebraic K"ahler sigma model with fermions, extending previous work on the $ ext{CP}^1$ model to its deformed version, and analyzes saddle points and quantum ambiguities.

Contribution

It extends the analysis of trans-series and saddle point contributions from the $ ext{CP}^1$ model to a deformed Lie-algebraic K"ahler sigma model with fermions, highlighting the role of the elongation parameter.

Findings

Ambiguity structures persist in the deformed model.

Saddle point solutions contribute to ground state energy expansions.

The elongation parameter influences higher-loop quantum corrections.

Abstract

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.