Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}P^{N-1}$ Models

Understand

We discuss the non-perturbative contributions from real and complex saddle point solutions in the $\mathbb{C}P^1$ quantum mechanics with fermionic degrees of freedom, using the Lefschetz thimble formalism beyond the gaussian approximation.

• We find bion solutions, which correspond to (complexified) instanton-antiinstanton configurations stabilized in the presence of the fermionic degrees of freedom.
• By computing the one-loop determinants in the bion backgrounds, we obtain the leading order contributions from both the real and complex bion solutions.
• To incorporate quasi zero modes which become nearly massless in a weak coupling limit, we regard the bion solutions as well-separated instanton-antiinstanton configurations and calculate a complexified quasi moduli integral based on the Lefschetz thimble formalism.