Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor

Abstract

We find a Chern-Simons propagator on the ball with the chiral boundary condition. We use it to study perturbatively Chern-Simons boundary conditions related to 2-dim $\sigma$-models and to Poisson-Lie T-duality. In particular, we find their renormalization group flow, given by the generalized Ricci tensor. Finally we briefly discuss what happens when the Chern-Simons theory is replaced by a Courant $\sigma$-model or possibly by a more general AKSZ model.

arXiv comment16 pages

References in corpus (3)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Remarks on Chern-Simons invariants

Cited by in corpus (7)

• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Duality invariant string beta functions at two loops
• On the Equivalence of Generalized Ricci Curvatures
• Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• Quantizing Derived Mapping Stacks