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

TL;DR

This paper investigates the renormalization group flow of Chern-Simons boundary conditions, connecting them to 2D sigma-models and Poisson-Lie T-duality, and explores their relation to generalized Ricci tensors and extended models.

Contribution

It introduces a perturbative analysis of Chern-Simons boundary conditions, deriving their RG flow as a generalized Ricci tensor, and discusses extensions to Courant sigma-models and AKSZ models.

Findings

Derived the Chern-Simons propagator with chiral boundary conditions.

Established the RG flow of boundary conditions as a generalized Ricci tensor.

Explored extensions to Courant sigma-models and AKSZ models.

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.