RST model

{{short description|Conformal anomaly free CGHS model}}

The Russo–Susskind–Thorlacius model

{{cite journal | last1 = Russo | first1 = Jorge | authorlink1 = Jorge Russo | last2 = Susskind | first2 = Leonard | authorlink2 = Leonard Susskind

| last3 = Thorlacius

| first3 = Lárus

| authorlink3 = Lárus Throlacius | date = 15 Oct 1992 | title = The Endpoint of Hawking Evaporation

| journal = Physical Review | volume = 46 | issue = 8 | pages = 3444–3449

| doi = 10.1103/PhysRevD.46.3444

| pmid = 10015289 | arxiv = hep-th/9206070

| bibcode = 1992PhRvD..46.3444R

| s2cid = 184623 }}

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

:$S\_\{\backslash text\{CGHS\}\}\; =\; \backslash frac\{1\}\{2\backslash pi\}\; \backslash int\; d^2x\backslash ,\; \backslash sqrt\{-g\}\backslash left\backslash \{\; e^\{-2\backslash phi\}\; \backslash left[\; R\; +\; 4\backslash left(\; \backslash nabla\backslash phi\; \backslash right)^2\; +\; 4\backslash lambda^2\; \backslash right]\; -\; \backslash sum^N\_\{i=1\}\; \backslash frac\{1\}\{2\}\backslash left(\; \backslash nabla\; f\_i\; \backslash right)^2\; \backslash right\backslash \}$, the following term

:$S\_\{\backslash text\{RST\}\}\; =\; -\; \backslash frac\{\backslash kappa\}\{8\backslash pi\}\; \backslash int\; d^2x\backslash ,\; \backslash sqrt\{-g\}\; \backslash left[\; R\backslash frac\{1\}\{\backslash nabla^2\}R\; -\; 2\backslash phi\; R\; \backslash right]$

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,

:$S\_\{\backslash text\{RST\}\}\; =\; -\backslash frac\{\backslash kappa\}\{\backslash pi\}\; \backslash int\; dx^+\backslash ,dx^-\; \backslash left[\; \backslash partial\_+\; \backslash rho\; \backslash partial\_-\; \backslash rho\; +\; \backslash phi\; \backslash partial\_+\; \backslash partial\_-\; \backslash rho\; \backslash right]$.

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.