RST model

Short description: Conformal anomaly free CGHS model

The Russo–Susskind–Thorlacius model or RST model in short is a modification of the CGHS model to take care of conformal anomalies and render it analytically soluble. In the CGHS model, if we include Faddeev–Popov ghosts to gauge-fix diffeomorphisms in the conformal gauge, they contribute an anomaly of -24. Each matter field contributes an anomaly of 1. So, unless N=24, we will have gravitational anomalies. To the CGHS action

$S_{\text{CGHS}}=\frac{1}{2\pi }\int d^{2}x\sqrt{-g}\{e^{-2\varphi }[R+4{\left(\mathrm{\nabla }\varphi \right)}^2+4{\lambda }^2]-\sum _{i=1}^N\frac{1}{2}{\left(\mathrm{\nabla }{f}_i\right)}^2\}$, the following term

$S_{\text{RST}}=-\frac{\kappa }{8\pi }\int d^{2}x\sqrt{-g}[R\frac{1}{{\mathrm{\nabla }}^2}R-2\varphi R]$

is added, where κ is either $(N-24)/12$ or $N/12$ depending upon whether ghosts are considered. The nonlocal term leads to nonlocality. In the conformal gauge,

$S_{\text{RST}}=-\frac{\kappa }{\pi }\int d{x}^{+}d{x}^{-}[{\partial }_{+}\rho {\partial }_{-}\rho +\varphi {\partial }_{+}{\partial }_{-}\rho ]$.

It might appear as if the theory is local in the conformal gauge, but this overlooks the fact that the Raychaudhuri equations are still nonlocal.