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Kevin_Axion
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What theories of quantum gravity are currently UV complete?
nrqed said:Could someone tell me (or give a reference explaining) what is the precise definition of a theory that is UV complete? Thanks.
nrqed said:Could someone tell me (or give a reference explaining) what is the precise definition of a theory that is UV complete? Thanks.
Finbar said: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.
atyy said: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.
nrqed said: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.
atyy said: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).
Quantum gravity is a theoretical framework that aims to unify the theories of general relativity and quantum mechanics. It seeks to explain the behavior of gravity at a quantum level, where the laws of physics are different from those at the macroscopic scale.
The UV complete problem refers to the inability of current quantum gravity theories to provide a complete description of the universe at the smallest scales, known as the Planck scale. These theories break down and give nonsensical results when applied to this scale.
Being UV complete means that a theory can accurately describe the behavior of particles and forces at all energy levels, including the Planck scale. This is crucial for a complete understanding of the universe, as it allows us to make predictions and test the theory at all scales.
There are many different approaches to solving the UV complete problem, including string theory, loop quantum gravity, and causal dynamical triangulation. Scientists use mathematical models and experiments to test these theories and see which one best describes the universe at all scales.
A successful UV complete quantum gravity theory would have profound implications for our understanding of the universe and could potentially lead to new technologies and advancements in science. It could also help solve some of the biggest mysteries in physics, such as the nature of dark matter and dark energy.