2025/09/05 by Christian Ferko, Michele Galli, Ferko, Christian +5
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2509.05081
openalex publication_date 2025/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The \mathbbCPN-1 model is an analytically tractable 2d quantum field theory which shares several properties with 4d Yang-Mills theory. By virtue of its classical integrability, this model also admits a family of integrable higher-spin auxiliary field deformations, including the T T deformation as a special case. We study the \mathbbCPN-1 model and its deformations from a geometrical perspective, constructing their soliton surfaces and recasting physical properties of these theories as statements about surface geometry. We examine how the T T flow affects the unit constraint in the \mathbbCPN-1 model and prove that any solution of this theory with vanishing energy-momentum tensor remains a solution under analytic stress tensor deformations -- an argument that extends to generic dimensions and instanton-like solutions in stress tensor flows including the non-analytic, 2d, root-T T case and classes of higher-spin, Smirnov-Zamolodchikov-type, deformations. Finally, we give two geometric interpretations for general T T-like deformations of symmetric space sigma models, showing that such flows can be viewed as coupling the undeformed theory to a unit-determinant field-dependent metric, or using a particular choice of moving frame on the soliton surface.