I Self-Dual Gravity and self-dual Yang Mills

[kodama]

this paper came out today

https://arxiv.org/abs/1610.01457
Self-Dual Gravity
Kirill Krasnov
(Submitted on 5 Oct 2016)
Self-dual gravity is a diffeomorphism invariant theory in four dimensions that describes two propagating polarisations of the graviton and has a negative mass dimension coupling constant. Nevertheless, this theory is not only renormalisable but quantum finite, as we explain. We also collect various facts about self-dual gravity that are scattered across the literature.

there is also an extensive literature on self-dual loop quantum gravity, when y=i

the paper states self-dual gravity, but makes no mention of self-dual loop quantum gravity, claims self-dual gravity is analogous to self-dual yang mills, and is finite as is the only native 4-d gravity whose quantum version in pure gravity that is finite

says string theory could be finite in 4d with compactification but also predicts infinite number of fields.

self-dual also has connections with penrose twistor theory.

what is current evaluation of self dual gravity and why does it get so little mention? krasnov claims it is finite quantum version in 4 d.

what is current evaluation of self-dual yang mills and can the SM be rewritten in a self-dual yang mills theory?

 

[mitchell porter]

According to the paper: "self-dual gravity" should be called anti-self-dual gravity. It is what you get, if you take the Weyl tensor component of space-time curvature, divide it into self-dual and anti-self-dual parts, and set the self-dual part to zero. In a realistic world of three space and one time dimensions, this guarantees that the other part must be zero too, so by itself it cannot describe the real world. It's interesting because of its mathematical properties, and the possibility that real gravity could be described by self-dual gravity plus something extra.

 

[kodama]

According to the paper: "self-dual gravity" should be called anti-self-dual gravity. It is what you get, if you take the Weyl tensor component of space-time curvature, divide it into self-dual and anti-self-dual parts, and set the self-dual part to zero. In a realistic world of three space and one time dimensions, this guarantees that the other part must be zero too, so by itself it cannot describe the real world. It's interesting because of its mathematical properties, and the possibility that real gravity could be described by self-dual gravity plus something extra.

what would be that something extra?

 

[mitchell porter]

what would be that something extra?

According to Herfray and Krasnov, the quadratic term from "topological gravity".