RST 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 CGHS = 1 2 π ∫ d 2 x − g { e − 2 ϕ [ R + 4 ( ∇ ϕ ) 2 + 4 λ 2 ] − ∑ i = 1 N 1 2 ( ∇ f i ) 2 } {\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\}} , the following term S RST = − κ 8 π ∫ d 2 x − g [ R 1 ∇ 2 R − 2 ϕ R ] {\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]} is added, where κ is either ( N − 24 ) / 12 {\displaystyle (N-24)/12} or N / 12 {\displaystyle N/12} depending upon whether ghosts are considered. The nonlocal term leads to nonlocality. In the conformal gauge, S RST = − κ π ∫ d x + d x − [ ∂ + ρ ∂ − ρ + ϕ ∂ + ∂ − ρ ] {\displaystyle S_{\text{RST}}=-{\frac {\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.

Conformal anomaly free CGHS 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 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 π ∫ d 2 x − g { e − 2 ϕ [ R + 4 ( ∇ ϕ ) 2 + 4 λ 2 ] − ∑ i = 1 N 1 2 ( ∇ f i ) 2 } {\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\}} , the following term

S RST = − κ 8 π ∫ d 2 x − g [ R 1 ∇ 2 R − 2 ϕ R ] {\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]}

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

S RST = − κ π ∫ d x + d x − [ ∂ + ρ ∂ − ρ + ϕ ∂ + ∂ − ρ ] {\displaystyle S_{\text{RST}}=-{\frac {\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

[edit]

1. ^ Russo, Jorge; Susskind, Leonard; Thorlacius, Lárus (15 Oct 1992). "The Endpoint of Hawking Evaporation". Physical Review. 46 (8): 3444–3449. arXiv:hep-th/9206070. Bibcode:1992PhRvD..46.3444R. doi:10.1103/PhysRevD.46.3444. PMID 10015289. S2CID 184623.

This relativity-related article is a stub. You can help Wikipedia by adding missing information.

• v
• t
• e