The Russo–Susskind–Thorlacius model[1] 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
, the following term
is added, where κ is either or depending upon whether ghosts are considered. The nonlocal term leads to nonlocality.
In the conformal gauge,
.
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.
![{\displaystyle S_{\text{CGHS}}={\frac {1}{2\pi }}\int d^{2}x\,{\sqrt {-g}}\left\{e^{-2\phi }\left[R+4\left(\nabla \phi \right)^{2}+4\lambda ^{2}\right]-\sum _{i=1}^{N}{\frac {1}{2}}\left(\nabla f_{i}\right)^{2}\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af8c5349300a00a59edd271eea445bc9b9e8a50a)
![{\displaystyle S_{\text{RST}}=-{\frac {\kappa }{8\pi }}\int d^{2}x\,{\sqrt {-g}}\left[R{\frac {1}{\nabla ^{2}}}R-2\phi R\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dcda2dd0ad6bb6770054188c91881f721977a9e)
![{\displaystyle S_{\text{RST}}=-{\frac {\kappa }{\pi }}\int dx^{+}\,dx^{-}\left[\partial _{+}\rho \partial _{-}\rho +\phi \partial _{+}\partial _{-}\rho \right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cabb0ef64f311da1c94338e7047fd24e8e17f9e5)