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The '''Russo-Susskind-Thorlacius model'''<ref>
{{cite journal | last1        = Russo | first1      = Jorge | authorlink1  = Jorge Russo | last2        = Susskind | first2      = Leonard | authorlink2  = Leonard Susskind
| last3        = Thorlacius
| first3      = L&aacute;rus
| authorlink3  = L&aacute;rus Throlacius | date        = 15 Oct 1992 | title        = The Endpoint of Hawking Evaporation
| journal      = Physical Review | volume      = 46 | issue        = 8 | series      = D | pages        = 3444–3449
| doi          = 10.1103/PhysRevD.46.3444
| url          = http://link.aps.org/doi/10.1103/PhysRevD.46.3444 | archiveurl  = http://arxiv.org/abs/hep-th/9206070 | archivedate  = 17 June 1992|arxiv = hep-th/9206070 |bibcode = 1992PhRvD..46.3444R }}
</ref> or '''RST model''' in short is a modification of the [[CGHS model]] to take care of [[conformal anomaly|conformal anomalies]]. In the CGHS model, if we include [[Faddeev-Popov ghost]]s 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 anomaly|gravitational anomalies]].
To the CGHS action
:<math>S_{\text{CGHS}} = \frac{1}{2\pi} \int d^2x\, \sqrt{-g}\left\{ e^{-2\phi} \left[ R + 4\left( \nabla\phi \right)^2 + 4\lambda^2 \right] - \sum^N_{i=1} \frac{1}{2}\left( \nabla f_i \right)^2 \right\}</math>, the following term
:<math>S_{\text{RST}} = - \frac{\kappa}{8\pi} \int d^2x\, \sqrt{-g} \left[ R\frac{1}{\nabla^2}R - 2\phi R \right]</math>
is added, where ''&kappa;'' is either <math>(N-24)/12</math> or <math>N/12</math> depending upon whether or not ghosts are considered. The nonlocal term leads to [[nonlocality]].
In the conformal gauge,
:<math>S_{\text{RST}} = -\frac{\kappa}{\pi} \int dx^+\,dx^- \left[ \partial_+ \rho \partial_- \rho + \phi \partial_+ \partial_- \rho \right]</math>.
 
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 ==
<references />
 
{{theories of gravitation}}
{{quantum gravity}}
 
{{relativity-stub}}
 
[[Category:Anomalies in physics]]
[[Category:Conformal field theory]]
[[Category:General relativity]]

Revision as of 22:11, 29 May 2013

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

SCGHS=12π∫d2x−g{e−2ϕ[R+4(∇ϕ)2+4λ2]−∑i=1N12(∇fi)2}, the following term
SRST=−κ8π∫d2x−g[R1∇2R−2ϕR]

is added, where κ is either (N−24)/12 or N/12 depending upon whether or not ghosts are considered. The nonlocal term leads to nonlocality. In the conformal gauge,

SRST=−κπ∫dx+dx−[∂+ρ∂−ρ+ϕ∂+∂−ρ].

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

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Template:Theories of gravitation Template:Quantum gravity

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