Gravity-Yang-Mills-Higgs unification bid by Krasnov and Gomez

[marcus]

Atyy spotted this paper yesterday
http://arxiv.org/abs/0911.3793
Gravity-Yang-Mills-Higgs unification by enlarging the gauge group
Alexander Torres-Gomez, Kirill Krasnov (University of Nottingham)
(Submitted on 19 Nov 2009)
"We revisit an old idea that gravity can be unified with Yang-Mills theory by enlarging the gauge group of gravity formulated as gauge theory. Our starting point is an action that describes a generally covariant gauge theory for a group G. The Minkowski background breaks the gauge group by selecting in it a preferred gravitational SU(2) subgroup. We expand the action around this background and find the spectrum of linearized theory to consist of the usual gravitons plus Yang-Mills fields charged under the centralizer of the SU(2) in G. In addition, there is a set of Higgs fields that are charged both under the gravitational and Yang-Mills subgroups. These fields are generically massive and interact with both gravity and Yang-Mills sector in the standard way. The arising interaction of the Yang-Mills sector with gravity is also standard. Parameters such as the Yang-Mills coupling constant and Higgs mass arise from the potential function defining the theory. Both are realistic in the sense explained in the paper."

The paper is a deep and beautiful completion of the program Krasnov has worked on for two years 2007-2009, and also it is a beginning.

Now he and collaborators will have to see if/how they can include fermions.

 

[atyy]

It's interesting they mention Percacci's old work in their line of descent.

They also talk about Asymptotic Safety, but in their enlarged space of theories with the same number of propagating degrees of freedom.

Edit: I didn't get that quite right. Let me quote their discussion instead.

"... Finally, let us briefly touch on the question of quantization. The theory we have considered was classical, but, of course, it has to be quantized. It is then clear that our action (1) is nonrenormalizable in the usual sense of the word. ... This is, of course, as expected, for we cannot hope to bring together a non-renormalizable theory (gravity) with renormalizable other interactions in a renormalizable unified theory. At best, we can hope for a non-renormalizable unified theory, and this is what is happening in our scenario.

At the same time, what our starting action (1) describes is just the most general generally covariant gauge theory. For this reason it can be expected that the class of theories (1) obtained by considering all possible potentials f(·) is closed under renormalization. ... Thus, at least prior to any concrete analysis, it seems that the sought UV completion may be given by the topological BF theory, something that in the past has been suggested in the literature in other contexts. All in all, the absence of the usual ”finite number of counterterms” renormalizability of our theory may not be a problem as the theory may possibly be renormalizable in the sense of Weinberg [28] as containing all possible counterterms, see also [29] for a more modern exposition of the notion of ”effective renormalizability”."

 

[Entropia]

It is a very hard problem, and the paper is an important step towards a complete theory of quantum gravity.

Their approach of unifying gravity, Yang-Mills theory, and the Higgs mechanism by enlarging the gauge group is a novel and intriguing idea. It is impressive that they were able to derive the standard graviton and Yang-Mills fields, as well as introducing Higgs fields that interact with both sectors in a natural way.

It will be interesting to see if they can extend their theory to include fermions, as this is a crucial component in any complete theory of quantum gravity. The potential for this theory to provide a more comprehensive understanding of the fundamental forces in nature is exciting and warrants further exploration.

Overall, this paper presents a compelling and well-developed argument for the unification of gravity and Yang-Mills theory, and I look forward to seeing how this theory progresses in the future.