# Color Kinematics Duality and Asymptotic Safety

• erkokite
In summary, the conversation discusses the concept of color-kinematic duality and its potential implications for quantum gravity. It is suggested that this duality may imply an equivalence between Yang Mills and non-SUGRA Einstein gravity, and that there may be a Gaussian fixed point where the cosmological constant and Newton's constant go to zero. This is compared to the Asymptotic Safety scenario, where there is also a Gaussian fixed point. However, it is noted that these two fixed points are derived using different methods and it is unclear if there is a deeper connection between them. Additionally, the conversation mentions that color-kinematic duality is not about showing that Einstein gravity is the exact same theory as Yang-Mills theory and that being a
erkokite
So, you'll have to forgive me, but I am an engineer, not a physicist, but I take an interest in quantum gravity. My understanding is primarily conceptual, not mathematical. So if my question is dumb, I apologize. Ok, here goes:

I'm aware of Zwi Bern's conjectured color-kinematics duality where the color factors of the scattering matrix of a Yang Mills theory are replaced with "kinematic factors," by which one obtains an equivalent SUGRA theory. This procedure can be performed to draw an equivalence between Yang Millks and non-SUGRA Einstein gravity (N=0) with an axion and a dilaton, which are regarded as unphysical and are canceled via ghost fields. A nice slideshow is available here showing the rough outline of the procedure:
http://media.scgp.stonybrook.edu/presentations/20131210_Johansson.pdf

If this procedure holds water, would it not imply that Einstein gravity when quantized is equivalent to a Yang Mills theory, and therefore asymptotically free? That is, it would possesses a gaussian fixed point where the cosmological constant and Newton's constant go to zero?

This reminded me a little of the Asymptotic Safety scenario where there is both a Gaussian and non-Gaussian fixed point along a certain RG trajectory for Quantum Einstein Gravity.
http://iopscience.iop.org/1367-2630/focus/Focus on Quantum Einstein Gravity
Look at the Type IIa trajectory in the diagram that passes through the origin.

So what I'm thinking is that it seems that in both cases (i.e. Color/Kinematics and Asymsafe) there exists a Gaussian Fixed Point. This result is derived using two fundamentally different methods.

So I guess what I'm asking is- is there correspondence between the two fixed points derived via two different means? Are they truly the "same" fixed point? Is there a deeper connection here? Some fundamental truth about the RG behavior of gravity, or is it just coincidence?

A gauge theory is said to have color-kinematic duality, if scattering amplitudes can be written in a form like that in Johansson's slide 4 - where there is a fraction with two factors in the numerator, a color factor and a kinematic factor, with the property that the possible color factors and the possible kinematic factors each separately obey the same algebraic relations.

Then, if you replace the color factor with another copy of the kinematic factor, you get amplitude formulas for a theory containing gravity. But it's not the same theory as the gauge theory. Most "dualities" are about having two or more ways to describe the same thing, but this one is about two different theories having a mathematical similarity.

So it's not about showing that Einstein gravity is the exact same theory as some Yang-Mills theory. Also, just being a Yang-Mills theory doesn't imply asymptotic freedom. That is just one possible type of RG behavior.

I am skeptical of the asymptotic safety program. Jacques Distler has blogged several strong criticisms of its methods and claims, and it also seems to be inconsistent with conventional black hole thermodynamics.

But it does look like the double copy relation pioneered by Bern et al, is relevant to RG behavior. Various supergravity theories are proving to be better behaved than naive analysis indicated, and it's partly because hidden properties of the amplitudes, like color-kinematic duality, cause unanticipated cancellations of divergences.

## 1. What is Color Kinematics Duality?

Color Kinematics Duality is a fundamental principle in theoretical physics that relates the mathematical structures of color and kinematics in gauge theories. It states that the color-ordered amplitudes in a gauge theory can be mapped onto kinematical quantities in a gravity theory, leading to a deeper understanding of the underlying physics.

## 2. What is Asymptotic Safety?

Asymptotic Safety is a concept in quantum field theory that refers to the existence of a non-trivial ultraviolet fixed point, where the theory becomes well-defined and free from divergences. This allows for the consistent formulation of a quantum field theory at arbitrarily high energies, making it a potential candidate for a theory of everything.

## 3. How are Color Kinematics Duality and Asymptotic Safety related?

Color Kinematics Duality and Asymptotic Safety are both important concepts in theoretical physics, but they are not directly related. However, there have been recent studies exploring the potential connection between the two, such as the idea that Asymptotic Safety could lead to a deeper understanding of the underlying principles behind Color Kinematics Duality.

## 4. What are the applications of Color Kinematics Duality and Asymptotic Safety?

The applications of Color Kinematics Duality and Asymptotic Safety are wide-ranging and still being explored. Some potential applications include gaining a better understanding of the fundamental laws of nature, developing a theory of quantum gravity, and potentially solving long-standing problems in theoretical physics such as the hierarchy problem and the unification of the fundamental forces.

## 5. What are the current challenges and controversies surrounding Color Kinematics Duality and Asymptotic Safety?

While there has been much progress made in understanding both Color Kinematics Duality and Asymptotic Safety, there are still many challenges and controversies surrounding these concepts. Some of the main challenges include developing a consistent mathematical framework for Asymptotic Safety and understanding the fundamental origin of Color Kinematics Duality. Additionally, there are ongoing debates and discussions about the validity and applicability of these concepts in different areas of theoretical physics.

Replies
8
Views
2K
Replies
2
Views
2K
Replies
29
Views
6K
Replies
2
Views
3K
Replies
14
Views
4K
Replies
1
Views
4K
Replies
2
Views
4K
Replies
3
Views
3K
Replies
21
Views
6K
Replies
2
Views
3K