TheRusso–Susskind–Thorlacius model^[1] orRST model in short is a modification of theCGHS model to take care ofconformal anomalies and render it analytically soluble. In the CGHS model, if we includeFaddeev–Popov ghosts to gauge-fix diffeomorphisms in theconformal gauge, they contribute an anomaly of -24. Each matter field contributes an anomaly of 1. So, unless N=24, we will havegravitational anomalies.To the CGHS action

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

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

is added, whereκ is either${\displaystyle (N-24)/12}$ or${\displaystyle N/12}$ depending upon whether ghosts are considered. The nonlocal term leads tononlocality.In the conformal gauge,

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

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.

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