RST model

Key takeaways

RST model belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect RST model to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of RST model from memory before moving on to harder problems.

Reference excerpt

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.

References

Worked examples

Example 1 — a first encounter with RST model

Start with the simplest possible case. Write down what RST model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to RST model before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about RST model ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of RST model

In research: RST model appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses RST model in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: RST model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Anomalies (physics), Conformal field theory, General relativity, so understanding it makes those chapters shorter.
In everyday life: Look for RST model outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study RST model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what RST model means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain RST model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is RST model in simple terms?

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…

Why does RST model matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study RST model?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on RST model.