From Self-Dual to Physical ℂPN−1: Anomalies, Boundary Stokes Phenomenon, and Global Structure of θ-vacua
Abstract
We introduce a two-coupling generalization of ℂPN−1 model that continuously interpolates between the self-dual (ε=0) and the physical (ε=g) theories as a useful nonperturbative tool. At ε≠ g, this model possesses a chiral imbalance, which may be viewed as a real topological deformation (imaginary-θ). We demonstrate that exact quantum equivalence between first- and second-order formulations strictly requires a topological counterterm sourced by a bosonic chiral anomaly. Solving this deformed theory at large N yields two primary results. First, we analytically determine the nonperturbative vacuum structure of the self-dual theory, a self-dual vacuum with a dynamically generated field-strength condensate. Second, we resolve a fundamental paradox where saddles with (θ+ 2πn) ∼ O(N) (n is branch number) spuriously yield lower energy densities than the physical ground state. Because the effective action possesses an essential singularity at F=0, we show that the Lefschetz thimble analysis must be generalized to include boundary thimbles. A boundary Stokes phenomenon renders the problematic saddles topologically inactive, fully restoring the validity of the large-N expansion for strongly coupled theories.
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BibTeX
@misc{hayashi2026from,
title = {{From Self-Dual to Physical $\mathbbCP^N-1$: Anomalies, Boundary Stokes Phenomenon, and Global Structure of $θ$-vacua}},
author = {Yui Hayashi and Mithat Ünsal},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30160},
eprint = {2608.30160},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30160},
}
RIS
TY - UNPB
TI - From Self-Dual to Physical ℂP^N−1: Anomalies, Boundary Stokes Phenomenon, and Global Structure of θ-vacua
AU - Yui Hayashi
AU - Mithat Ünsal
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30160
UR - https://arxiv.org/abs/2608.30160
AB - We introduce a two-coupling generalization of ℂP^N−1 model that continuously interpolates between the self-dual (ε=0) and the physical (ε=g) theories as a useful nonperturbative tool. At ε≠ g, this model possesses a chiral imbalance, which may be viewed as a real topological deformation (imaginary-θ). We demonstrate that exact quantum equivalence between first- and second-order formulations strictly requires a topological counterterm sourced by a bosonic chiral anomaly. Solving this deformed theory at large N yields two primary results. First, we analytically determine the nonperturbative vacuum structure of the self-dual theory, a self-dual vacuum with a dynamically generated field-strength condensate. Second, we resolve a fundamental paradox where saddles with (θ+ 2πn) ∼ O(N) (n is branch number) spuriously yield lower energy densities than the physical ground state. Because the effective action possesses an essential singularity at F=0, we show that the Lefschetz thimble analysis must be generalized to include boundary thimbles. A boundary Stokes phenomenon renders the problematic saddles topologically inactive, fully restoring the validity of the large-N expansion for strongly coupled theories.
ER -