Complex nonlinear sigma model

Abstract:Motivated by the recent interest in the criticality of open quantum many-body systems, we study nonlinear sigma models with complexified couplings as a general framework for nonunitary field theory. Applying the perturbative renormalization-group analysis to the tenfold symmetric spaces, we demonstrate that fixed points with complex scaling dimensions and critical exponents arise generically, without counterparts in conventional nonlinear sigma models with real couplings. We further clarify the global phase diagrams in the complex-coupling plane and identify both continuous and discontinuous phase transitions. Our work thus identifies nonlinear sigma models as a representative setting for studying complex critical points and elucidates universal aspects of critical phenomena in complexified field theory.

Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

arXiv:2601.20166 [cond-mat.stat-mech]

(or arXiv:2601.20166v2 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2601.20166 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1103/dmvx-zg1v Focus to learn more DOI(s) linking to related resources

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