Gauged Courant sigma models
Noriaki Ikeda
TL;DR
Gauged Courant Sigma Models (GCSMs) extend the Courant sigma model within the AKSZ/BV framework by promoting global target-space symmetries to local gauge symmetries. The authors develop a hierarchy of gauged theories using Lie algebroid and Courant algebroid data, introducing covariant coordinates and connections to realize gauging, and deriving covariant homological functions $\Theta^{\nabla}$ whose nilpotency $\{\Theta^{\nabla},\Theta^{\nabla}\}=0$ imposes geometric flatness conditions (e.g., $R=0$, ${}^A S=0$, ${}^E S=0$, $\nabla\rho=0$, ${}^A\nabla H=0$). They provide explicit AKSZ actions for standard and general SCSMs with both Lie algebroid and Courant algebroid gauging, and show how flux deformations ($\Theta_F$) and boundary terms ($S_b$) deform the master equation and lead to generalized momentum- or homotopy-momentum structures on boundaries. The framework unites equivariant and gauged AKSZ theories and sets the stage for further quantization and global symmetry analysis in the presence of fluxes and boundaries. Overall, the paper establishes a comprehensive geometric construction of GCSMs and clarifies the consistency conditions required for their BV/AKSZ formulations.
Abstract
We propose a new class of sigma models based on Courant sigma models. We refer to these models as gauged Courant sigma models (GCSMs). By introducing additional gauge symmetries, such as those associated with a Lie group, a Lie groupoid (or Lie algebroid), and a Courant algebroid on the target space, Courant sigma models are extended to gauged sigma models of AKSZ type. The consistency of the theory is ensured by identities among geometric quantities on Lie algebroids and Courant algebroids, such as curvatures and torsions, which can be interpreted as flatness conditions on the target space. We also analyze geometric structures of GCSMs in the presence of fluxes and boundaries.