Geometric Unity update

Eric Weinstein recently gave a talk extending his theory of everything to include a 4-dimensional cosmological constant. I tried to post about it on one of the subreddits about his work (/r/theportal), but they seem to have new moderation rules. Hopefully I can get through, but for now I post my remarks here:. 

Dark sector from duality invariance

I was just skimming a new paper on how to state "duality invariant" theories, like electromagnetism with both electric and magnetic charges. In talking about the 6d (2,0) family of theories, it says (equation 4.1) that an auxiliary vector field that breaks Lorentz covariance is often needed, in order to make the overall theory Lorentz-invariant. This immediately reminded me e.g. of the "impostor field" appearing in a form of modified gravity due to Sabine Hossenfelder, and which has been used to model MOND. Can the auxiliary vector field of the duality-invariant theories be used in this way?

Qutritzer fine structure

Last month I ran across an alleged quantum-gravitational bound on the fine structure constant (proposed by Shahar Hod) that is remarkably close to the actual value. I am somewhat surprised that it has received almost no public attention, but there are many examples of neglected ideas and observations, inside and outside physics. 

The actual "bound" is ln(3)/(48pi). As I describe in the linked post, this work is descended from an episode in black hole physics from over twenty years ago, in which the quantity ln(3) showed up in the "quasinormal" resonant modes of charged near-extremal black holes. (Carl Brannen says the quasinormal modes are associated with excited unbound states, which makes sense since they describe Hawking radiation, i.e. a quantum escaping from the black hole.) 

Today Scott Aaronson mentioned some results on how to efficiently distinguish three states of a qubit. I mused that maybe the current generation of "qubitzers" could take another look at the ln(3) mysteries, using tools from those results. (I spoke of "qutritzers", but I think technically this is not about qutrits, just about three states of a qubit.) 

Woit plus Weinstein

This is my latest fuzzy thought... Woit's theory ("Euclidean twistor unification") is a form of chiral graviweak unification. In such theories, a four-dimensional rotational symmetry is factored into left-handed and right-handed components, which become the gauge symmetries of the weak force and the gravitational force respectively. Woit goes further, considering a particular quotient bundle in twistor space, in order to obtain the hypercharge and color gauge symmetries as well. 

Some things are lacking in Woit's theory - like fermions, and three generations. But let's suppose he does have a way to obtain gravity and the standard model gauge fields, by looking at the twistor space of a 4d manifold in a particular way... If we switch back to Weinstein's Geometric Unity, it embeds a 4d manifold into a 14d manifold which is actually the metric bundle of the 4d manifold. Then we are to have a 14d Yang-Mills field coupled to the 4d manifold by a "shiab operator" in such a way as to somehow give us 4d gravity, and a 14d Dirac field that in 4d will give us two of the three fermion generations (with the heavy third generation to come as a piece of a 14d Rarita-Schwinger field). 

What interests me is whether Woit's construction can be obtained as a subset of Weinstein's. One reason to consider this, is that Weinstein also talks about obtaining gravity from an SL(2,C) subgroup of his complexified 14d gauge group - a group which also features in some chiral approaches to gravity. Unfortunately it is unclear to me how this related to the shiab operator, which is to mimic, for the 14d gauge field, the Ricci decomposition of the 4d metric. 

Schwarzschild mereology

Earlier this year it was claimed that Schwarzschild geometries (i.e. the classic black hole geometry) can be obtained by assembling a collection of Reissner-Nordstrom black holes held together by "struts" that resemble negative-tension strings. This is therefore a model for the microstates of a Schwarzschild black hole. 

(1) There's a somewhat fringe theory that black holes contain negative pressure that contributes to dark energy. I would want to look at that idea, also negative branes (associated with altered spacetime signatures), also how black holes are obtained in Matrix theory and Tom Banks's musings on how to obtain de Sitter space in a similar way. 

(2) As far as I know, we don't know how to obtain RN black holes in string theory? They can be approximated by JT gravity but UV completion not known. 

Nebulous

I had a thought today: what if Eric Weinstein's Geometric Unity, has a formulation as complex E8 gauge theory in 14 dimensions, coupled to a brane whose worldvolume theory is Gunaydin's 4d octonionic magic supergravity? The rationale for this being the 14-dimensional grading of E8(C), something which Michael Rios told me about years ago. 

It's unlikely, but a concrete speculation like this, is a way to get a handle on several otherwise nebulous possibilities. 

Wide binaries

 This is a placeholder post, for discussion of wide binaries.