Complex nonlinear sigma model

TL;DR

This paper investigates complex nonlinear sigma models as a framework for nonunitary field theories, revealing new fixed points and phase transitions relevant to quantum many-body systems.

Contribution

It introduces the analysis of nonlinear sigma models with complex couplings, demonstrating the emergence of fixed points with complex scaling dimensions and mapping global phase diagrams.

Findings

Fixed points with complex critical exponents are common in complexified models.

Identifies continuous and discontinuous phase transitions in the complex-coupling plane.

Provides insights into universal critical phenomena in nonunitary field theories.

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 elucidates universal aspects of critical phenomena in complexified field theory.