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I was looking at pdf file of the presentation of a conference talk. The speaker discusses two types of "mechanisms" for stabilizing the weak scale and calls them "weakly coupled" and "strongly coupled". The examples are:

Weakly coupled: SM with a light Higgs, SUSY, Little Higgs, Twin Higgs, Large extra dimensions, Universal extra dimensions.

Strongly Coupled: Technicolor, Topcolor, Top See Saw, Composite Higgs, Randall-Sundurm warped extra dimension models.

I need to understand what makes one such beyond standard model theory to be weakly coupled and another to be strongly coupled, in general and especially why large/universal extra dimension and Randall-Sundrum models belong to two separate groups.

Perhaps I should emphasize where my doubt is: I understand why theories like technicolour are thought to be "strongly coupled" but I do not at all understand why theories involving say Randall-Sundrum extra dimensional models are also so. When we say Randall-Sundrum warped extra dimension model, we mean a particular kind of background on which different types of interactions take place. But why should all interactions taking place in such a background will have to be strongly coupled? How does background spacetime decide whether an (or all) interaction(s) will be strongly coupled?

Or does this have anything to do with the fact that in (classical) GR, spacetime is dynamically determined and is coupled with matter and energy content of the universe and may be due to quantum gravity effects this strong/weak nature of interactions are/is manifested. But what is the way to explain that?

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Strongly coupled theories are those whose coupling constant is strong i.e. greater than a particular number of order of one, $g\gt {\mathcal O}(1)$. It means that perturbative expansions (and the leading simplest Feynman diagrams) are not good approximations for the most elementary physical processes that may occur in these theories. One must find other methods because the influence of quantum mechanics is important.

This is obviously the case for technicolor whose key processes depend on the confinment of the technicolor and confinement always means that the coupling is getting strong (and even stronger, arbitrarily stronger). But the other strongly coupled models in your list are analogous. On the other hand, the weakly coupled theories in your list are analogous to the Standard Model at high energies, a few leading terms i.e. simple Feynman diagrams are enough to get a good enough approximation.

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Strongly and Weakly Coupled Theories

Perturbative approaches to physics have had great success in providing a bridge between theory and experiment. The idea behind perturbation theory is expansion in terms of the coupling constant, the energy scale/strength of an interaction.

Strongly Coupled Theories are theories that have a coupling constant greater than 1. As a result, the perturbative series, i.e. the expansion, does not converge, so that makes perturbation theory nonsensical beyond the nonsensicality of the divergence of the Dyson series and renormalization. Quantum effects are too strong to be considered small enough in a way that allows us to expand their energy scale (coupling constant).

Weakly Coupled Theories, as the name suggests, are the opposite, and are thus very nice to work with, and a very "standardized" approach can be taken. The Standard Model as you mentioned enjoys this, as do some famous BSM theories that you also mention.

S-Duality

One of the cornerstones of String Theory is the notion of a duality. With notions like the S duality, T duality, and the resulting Kapustin duality, AdS/CFT duality, etc. Of particular interest is the S-Duality, or the strong-weak duality, which was first observed in electromagnetism:

The Interchange of Electric and Magnetic field (with a minus sign in natural units)

In an attempt to generalize this, Montonen and Olive discovered that in N=4 Yang-Mills, one has a correspondence between gauge groups and their Langlands dual groups, that have as their coupling constant, the inverse of the original theory's complexified coupling constant, in other words, an equivalence between strongly and weakly coupled theories.

Here is a paper on Seiberg Duality for more(S Duality in a specific context)

Randall-Sundrum Theories

RS theories have a Planckbrane, where Gravity is strong, and via AdS/CFT they have been shown to be dual to technicolor models, which of course are strongly coupled as per the confinement at their center. [1]

Spacetime and Coupling

Now with regard to your fascinating question on how background spacetime affects the coupling of a theory, we obviously need to think about how spacetime affects our theory, how warping affects energy scales, and what particles coupled with what other particles. For example, take an approach like RS, with highly warped spacetime, it follows that the graviton is strongly coupled in the regime of the Planckbrane, while it is weakly coupled in the Tevbrane. This gives you the intuition that higher-dimensional space does not inherently decide whether a theory is strongly or weakly coupled, but rather its dynamics do.

Quantum Gravity

Finally, I shall address your last question by mentioning that QG can induce self-interactions, which could drive up energy scales, but the coupling to gravitons should not intrinsically affect processes to a point where a transition between weak and strong coupling occurs in the TeVbrane, or in general.

Perhaps Useful Links:

Strongly Coupled Gauge Theory

QG induced self-interactions

IR Dependence of strong coupling in RS models

Overview of Related RS Properties

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