RST model
The Russo-Susskind-Thorlacius model[1] or RST model in short is a modification of the CGHS model to take care of conformal anomalies. 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^2x\, \sqrt{-g}\left\{ e^{-2\phi} \left[ R %2B 4\left( \nabla\phi \right)^2 %2B 4\lambda^2 \right] - \sum^N_{i=1} \frac{1}{2}\left( \nabla f_i \right)^2 \right\}](/2012-wikipedia_en_all_nopic_01_2012/I/4529ab034b1a3c58f4843d98e8982fb6.png)
, the following term![S_{\text{RST}} = - \frac{\kappa}{8\pi} \int d^2x\, \sqrt{-g} \left[ R\frac{1}{\nabla^2}R - 2\phi R \right]](/2012-wikipedia_en_all_nopic_01_2012/I/ca330c7bce5fc6f31fdbcefd7a1cd154.png)
is added, where κ is either 
or 
depending upon whether or not ghosts are considered. The nonlocal term leads to nonlocality. In the conformal gauge,
![S_{\text{RST}} = -\frac{\kappa}{\pi} \int dx^%2B\,dx^- \left[ \partial_%2B \rho \partial_- \rho %2B \phi \partial_%2B \partial_- \rho \right]](/2012-wikipedia_en_all_nopic_01_2012/I/2d632c75e124e9656c13999181c12e1e.png)
.
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.
References
- ^ Russo, Jorge; Susskind, Leonard; Thorlacius, Lárus (15 Oct 1992). "The Endpoint of Hawking Evaporation". Physical Review. D 46 (8): 3444–3449. doi:10.1103/PhysRevD.46.3444. Archived from the original on 17 June 1992. http://arxiv.org/abs/hep-th/9206070.