Quantum Gravity Theories: What is UV Complete?

[Kevin_Axion]

What theories of quantum gravity are currently UV complete?

 

[atyy]

AdS/CFT is thought to be UV complete. The CFT is definitely UV complete. The only question is whether the CFT is "fully dual" to string theory in an AdS space. Whatever "fully dual" could mean, the evidence in favour of such a conjecture is very strong, but there is no proof at the moment. Sometimes it is said that the CFT is the definition of the string theory, since the string theory doesn't have an independent definition to arbitrarily high energies.

 

[tom.stoer]

I guess that AS indicates that GR is UV complete, provided that the existence of a non-gaussian fixed point holds.

 

[mitchell porter]

Is there any evidence for asymptotic safety of general relativity? And how about evidence against?

 

[tom.stoer]

From what I read in the papers and from the AS FAQs I would say that there are indications that GR and generalizations of GR including some more f(R) terms beyond the first term R are indeed a. s.

http://www.percacci.it/roberto/physics/as/faq.html

Of course one can never prove this exactly, one can only use a truncation using finitly many f(R) terms and show that Gk² and the c.c. have finite values in the UV, and that all other terms have zero coupling. But of course this could change if one includes higher f(R) terms or terms of different structure. There are e.g. indications that ECT including the Holst term (which is related to LQG) has a different UV limit than GR.

 

[S.Daedalus]

How about Dvali's 'http://arxiv.org/abs/1005.3497" ' for a mechanism to make ordinary quantum general relativity UV complete?

 

[nrqed]

Could someone tell me (or give a reference explaining) what is the precise definition of a theory that is UV complete? Thanks.

 

[atyy]

Could someone tell me (or give a reference explaining) what is the precise definition of a theory that is UV complete? Thanks.

A UV complete theory is a theory that does not predict its own failure - ie. is mathematically consistent and requires experimental data for its falsification.

QCD is UV complete, but is experimentally false, because it doesn't contain gravity. Classical electromagentism without point particles is UV complete, because it is a consistent theory, but is experimentally false, because it doesn't contain quantum mechanics.

OTOH, the standard model is UV incomplete, because the Higgs and electromagnetic fields have Landau poles (also assuming that they aren't asymptotically safe, which hasn't been proved), so we know the theory is false, even without experiments.

 

[Finbar]

Could someone tell me (or give a reference explaining) what is the precise definition of a theory that is UV complete? Thanks.

I don't know that there is a precise definition. If we specialises to QFT's then the theory must be asymptotically safe or free. Which basically means that there are no unphysical divergencies at all energy scales in the theory and the theory only has finite many parameters that need to be fixed by experiment. Also the theory must be unitary which means that the theory must give probabilities for different out comes of experiments that add up to one.

These requirements are enough to ensure that the theory continues to make sense and gives predictions up to arbitrary high energies.

Theories which are not UV complete are called effective theories. These theories may only be unitary and predictive up to some energy scale. Above this scale new physics must enter. A good example is chiral perturbation theory which must be by Yang-Mills theory(QCD) at high energies.



In theories of gravity the problem of UV completion is related to gravity becoming strongly coupled at high energies. In general it is very hand to calculate when a theory is strongly coupled. String theory attempts to deal with this issue by using dualities so that gravity at high energies is dual to a theory which is weakly coupled.

 

[nrqed]

I don't know that there is a precise definition. If we specialises to QFT's then the theory must be asymptotically safe or free. Which basically means that there are no unphysical divergencies at all energy scales in the theory and the theory only has finite many parameters that need to be fixed by experiment. Also the theory must be unitary which means that the theory must give probabilities for different out comes of experiments that add up to one.

These requirements are enough to ensure that the theory continues to make sense and gives predictions up to arbitrary high energies.

Theories which are not UV complete are called effective theories. These theories may only be unitary and predictive up to some energy scale. Above this scale new physics must enter. A good example is chiral perturbation theory which must be by Yang-Mills theory(QCD) at high energies.

I am used to a different use of the term effective field theory. I see eft's as non-renormalizable theories which are therefore obviously valid within a restricted range of energy. I would not call QED an effective field theory since it is renormalizable. However it is not UV complete because of the Landau pole. I knew that QED was not considered UV complete despite being renormalizable and this is what prompted my question.
Would you call QED an effective field theory?

Thanks for your input.

 

[nrqed]

A UV complete theory is a theory that does not predict its own failure - ie. is mathematically consistent and requires experimental data for its falsification.

QCD is UV complete, but is experimentally false, because it doesn't contain gravity. Classical electromagentism without point particles is UV complete, because it is a consistent theory, but is experimentally false, because it doesn't contain quantum mechanics.

OTOH, the standard model is UV incomplete, because the Higgs and electromagnetic fields have Landau poles (also assuming that they aren't asymptotically safe, which hasn't been proved), so we know the theory is false, even without experiments.

Thanks for your input, atyy, I appreciate your time. I was thinking along those lines but wanted to make sure I was not mistaken.

 

[Finbar]

I am used to a different use of the term effective field theory. I see eft's as non-renormalizable theories which are therefore obviously valid within a restricted range of energy. I would not call QED an effective field theory since it is renormalizable. However it is not UV complete because of the Landau pole. I knew that QED was not considered UV complete despite being renormalizable and this is what prompted my question.
Would you call QED an effective field theory?

Thanks for your input.

Yes QED is an effective theory because its only valid up to some scale (as far as we know).
Its only a good theory at low energies.

I think its useful to understand the difference between perturbative renormalisability and non-perturbative renormalizability in light of asymptotic safety. QFT that are UV complete and can be made sense of at all energy scales are asymptotically free or safe these theories are "non-perturbativly renormalizable". QED is perturbativly renormalizable but not asymptotically free or safe(as far as we know). Gravity is not perturbativly renormalizable but it may well be asymptotically safe.

Your reason for thinking effective theories are non-perturbativly renormalizable probably comes from too many physicists thinking field theories only make sense perturbativly; asymptotic safety of e.g.the Gross-Neveu model in 2<d<4 is the counter example.

 

[atyy]

My understanding is the same as Finbar's that QED is an effective theory that breaks down at high energies, and so isn't UV complete. Its renormalizability is due to an IR fixed point, whereas a UV complete quantum field theory should have a UV fixed point (no Landau pole).

 

[tom.stoer]

Coming back to the original question: "What theories of quantum gravity are currently UV complete?"

It could very well be that the UV behavior of QED is modified (cured) due to its coupling to an (asymptotically safe) theory of quantum gravity. And of course it's possible that an asymptotically safe theory of quantum gravity loses this desired feature when coupled to QED.

 

[tom.stoer]

What about the status of LQG? I lost track and I am not sure sure if I know all relevant papers (wrong: I am pretty sure that I don't know the relevant papers :-) - and if they all agree :-)

 

[nrqed]

My understanding is the same as Finbar's that QED is an effective theory that breaks down at high energies, and so isn't UV complete. Its renormalizability is due to an IR fixed point, whereas a UV complete quantum field theory should have a UV fixed point (no Landau pole).

Thank you to both you and Finbar. Yes, I was being too narrow-minded in focusing on perturbative renormalizability. Thanks for setting me straight!


Regards