1998/06/30 by Alexander D. Popov, A. D. Popov
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Chern–Simons theory #Conformal field theory #Conformal map #Field (mathematics) #Gauge theory #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantization (signal processing) #String theory #Theoretical physics #hep-th
paper · pdf · doi:10.1016/s0550-3213(99)00227-8
published as Nucl.Phys. B550 (1999) 585-621 · 33 pages, LaTeX2e, corrected version
arxiv created 1998/09/07 · openalex publication_date 1999/06/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is well known that rational 2D conformal field theories are connected with Chern-Simons theories defined on 3D real manifolds. We consider holomorphic analogues of Chern-Simons theories defined on 3D complex manifolds (six real dimensions) and describe 4D conformal field theories connected with them. All these models are integrable. We describe analogues of the Virasoro and affine Lie algebras, the local action of which on fields of holomorphic analogues of Chern-Simons theories becomes nonlocal after pushing down to the action on fields of integrable 4D conformal field theories. Quantization of integrable 4D conformal field theories and relations to string theories are briefly discussed.