Gauged linear $\sigma$model and gauged Witten equation
Gauged linear $\sigma$model and gauged Witten equation

Guangbo Xu , UCI
Fine Hall 322
This is a joint work with Gang Tian. I will talk about the analytical properties of the classical equation of motion in gauged linear $\sigma$model, which we call the gauged Witten equation. This is a generalization of the Witten equation in LandauGinzburg Amodel (FanJarvisRuan, Witten) and the symplectic vortex equation (Mundet, CieliebakGaioSalamon). We will also discuss a mathematical definition of the correlation function, using the moduli space of gauged Witten equation, when the curve is fixed.