# From String theory to QFT & SM: What does AdS/CFT theory can do and what cann't do?

• Osiris
In summary, AdS/CFT and related dualities may not be able to generate a dynamical background, but this has yet to be fully proven.

#### Osiris

Can anyone please comment on this?

Any new progress in extending String theory to QFT & SM other than AdS/CFT?

The moniker ADS/CFT is a class of theories and often its pretty broad when utilized by physicists. When people aren't being specific, it means roughly conformal field theory and gravity dual. So nowdays you have all sorts of crazy promising conjectures floating around. Like CFT/DS and CFT/Kerr-Newman etc. A pretty long list!

Then there's all the old dualities (N vs 1/N), weak-strong, Electro-Magnetic dualities, etc etc

Can anybody explain if this class of dualities can solve the problem that string theory depends on the choice of some background metric? Can AdS/CFT or any related duality "generate" a dynamical background?

I would say NO because AdS IS a specific background!

This question keeps coming up and has been thoroughly discussed before in many threads going back about 7 years now. The punchline is it depends exactly what you mean when you refine the question into actual math.

On one hand there is nothing (modulo a caveat, see below) intrinsically fixed about ADS/CFT. Everything is dynamical in the gravitational side, eg the bulk itself is completely dictated by general relativity and the space is free to move and change. You can add matter and watch things curve and fluctuate in complicated ways and so forth, black holes arise and vanish etc etc. Meanwhile the CFT is fixed on some n-1 dimensional space although it can be defined nonperturbatively. So in a sense, using rather imprecise language, you have a dual between a background dependant formulation and a background independant one.

The one thing that does remain fixed on the gravtitational side is the choice of boundary conditions (or to be technically more correct, the superselection sector), but this is true in classical GR as well. For instance in a spacetime that is asymptotically ADS, you cannot force it to become flat (it takes an infinite amount of energy).

In a recent discussion at http://www.nonequilibrium.net/universal-properties-u1-current-deconfined-quantum-critical-points/ ,I became aware of the paper http://arxiv.org/abs/0806.0110 . Therein, the following statements are proven:

1. AdS/CFT makes a prediction for some quantities c’/c and k’/k, eqn (5).

2. This prediction is compared to the exactly known values for the 3D O(n) model at n = infinity, eqns (28) and (30).

3. The values disagree. Perhaps not by so much, but they are not exactly right.

The standare way of saying this is that the d-dimensional O(n) model does not have a classical gravitational dual, at least not in some neighborhood of n = infinity, d = 3, and hence not for generic n and d. There might be exceptional cases where a gravitational dual exist, e.g. the line d = 2, but generically it seems disproven by the above result. Also note that the O(n) model is one of the most important statphys models, which include the Ising, XY and Heisenberg models for n = 1, 2, 3.

I am on record of being skeptical about the physical relevance of AdS/CFT, but that was mainly because the premises do not seem to hold in nature: physical gravity lives in dS rather than AdS space, and physical QCD is asymptotically free rather than conformal. But the O(n) model at criticality is conformal, so the premises are satisfied, but the result is still wrong. If AdS/CFT does not apply to a CFT with infinitely many components or colors, when can it be trusted? And how do we know if it applies, if we don't have an exact solution to compare to?

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An important aspect about the AdS/CFT is that it can be regarded as a classical/quantum dualism.

In this description, quantum phenomena such as the spontaneous breaking
of the center of the gauge group, magnetic confinement, and the mass gap are coded in
classical geometry. E. Witten hep-th/9803131​

In AdS/QCD classical configuration of the fields in the AdS metric can reproduce non-perturbative QCD and the quantum running of the strong coupling constant.

This neglected aspect of AdS/CFT has been interpreted as coming from a deterministic theory, that is a fundamental classical field theory which effectively reproduces QM.

that's weird: as far as I understood AdS is the classical, background independent part and CFT is a quantum theory, but background dependent.

So unfortunastely it's not the combination we are lookinh for ...

What do you mean with CFT is background dependent. The background is the metric?

The CFT in d dim is dual to the AdS field theory in d+1 dim.
If you want you can say that the warped dimension is dynamical generated.

@haelfix: is there a paper from which I can understand the meaning of "background independence" in AdS/CFT?

thanks!

## 1. What is AdS/CFT theory?

AdS/CFT theory stands for Anti-de Sitter/Conformal Field Theory. It is a theoretical framework that describes the relationship between two seemingly different theories: Anti-de Sitter space, which is a concept from string theory, and Conformal Field Theory, which is a concept from quantum field theory.

## 2. How does AdS/CFT theory relate to string theory and quantum field theory?

AdS/CFT theory suggests that the two seemingly different theories, string theory and quantum field theory, are actually dual to each other. This means that they describe the same physical phenomena, but in different mathematical languages. AdS/CFT theory provides a way to translate between these two languages, allowing for a deeper understanding of both theories.

## 3. What can AdS/CFT theory do?

AdS/CFT theory has been used to make progress in several areas of physics, including black hole physics, quantum gravity, and condensed matter physics. It has also provided insights into the behavior of strongly interacting systems, which are notoriously difficult to study using traditional methods.

## 4. What can't AdS/CFT theory do?

While AdS/CFT theory has been successful in many areas of physics, it is not a complete theory of everything. It is limited in its ability to describe certain physical phenomena, such as the behavior of particles at the smallest scales. Additionally, it is a theoretical framework and still requires experimental validation.

## 5. How does AdS/CFT theory contribute to our understanding of the universe?

AdS/CFT theory has the potential to bridge the gap between two major theories in physics, string theory and quantum field theory. This could lead to a deeper understanding of the fundamental laws that govern our universe. Additionally, the insights gained from AdS/CFT theory have the potential to inform future experiments and observations, providing a way to test and refine our understanding of the universe.