RST model explained

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

S _{CGHS} = (1)/(2 \pi) \int d ^{2x} \sqrt{ - g}\left\{ e ^{-2\phi} \left[ R + 4 \left( \nabla\phi \right) ^{2} + 4λ ^{2} \right] - \sum ^{N} _{i =1} (1)/(2) \left( \nabla f _{i} \right) ^{2} \right\} , the following termS _{RST} = - (\kappa)/(8 \pi) \int d ^{2x} \sqrt{ - g} \left[ R (1)/(\nabla ^{2}) R - 2 \phi R \right] 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 _{RST} =- (\kappa)/(\pi) \int dx ^{+dx} ^{-} \left[ \partial _{+} \rho \partial _{-} \rho + \phi \partial _{+} \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.

References

1. Russo . Jorge . Jorge Russo . Susskind . Leonard . Leonard Susskind. Thorlacius. Lárus. Lárus Throlacius . 15 Oct 1992 . The Endpoint of Hawking Evaporation. Physical Review . 46 . 8 . 3444–3449. 10.1103/PhysRevD.46.3444. 10015289 . hep-th/9206070. 1992PhRvD..46.3444R. 184623 .