# Our world as a typical F-theory vacuum?

1. Nov 10, 2015

### mitchell porter

This paper presents an unusually concrete hypothesis about the string theory landscape - that it is numerically dominated by "flux vacua" arising from a single compactification manifold. And our world could be one of them.

http://arxiv.org/abs/1511.03209
The F-theory geometry with most flux vacua
Washington Taylor, Yi-Nan Wang
(Submitted on 10 Nov 2015)
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold ${\cal M}_{\rm max}$ gives rise to ${\cal O} (10^{272,000})$ F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of ${\cal O} (10^{-3000})$. The fourfold ${\cal M}_{\rm max}$ arises from a generic elliptic fibration over a specific toric threefold base $B_{\rm max}$, and gives a geometrically non-Higgsable gauge group of $E_8^9 \times F_4^8 \times (G_2 \times SU(2))^{16}$, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an $SU(5)$ GUT group on any further divisors in ${\cal M}_{\rm max}$, or even an $SU(2)$ or $SU(3)$, so the standard model gauge group appears to arise in this context only from a broken $E_8$ factor. The results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on ${\cal M}_{\rm max}$.

Last edited: Nov 10, 2015
2. Nov 11, 2015

### Staff: Mentor

I'm probably not the one whom you wanted to address since my knowledge here is basic at its best. Therefore my question: Did you post this as information for string theorists or as germ of a discussion? Do you want it to keep it under "unanswered"?
Am I right that I counted more than $10^{61}$ dimensions of this gauge group? That's a hell of a group.
If I'm allowed may I ask something general: Why are all gauge groups, except some small $SU(n)$ always exceptional Lie Groups? Is it because it has to be a Lie Group plus high coefficients, i.e. variability in the root system?

Last edited: Nov 11, 2015
3. Nov 20, 2015

### mitchell porter

It was meant for discussion...

Those Lie group factors in the "geometrically non-Higgsable gauge group" actually come from a geometric incarnation of the Dynkin diagrams. The "elliptic fourfold ${\cal M}_{\rm max}$" contains singularities which are what you would get if you started with a set of two-spheres touching each other with a topology encoded in a Dynkin diagram (point = sphere, edge = touching), and then shrank the sphere's volumes to zero. And I think the gauge field comes from D2-branes wrapping the two-spheres.

${\cal M}_{\rm max}$ is basically a Calabi-Yau space, such as you hear about in popular descriptions of string theory - a microscopic six-dimensional space which is to be understood as existing at each point in our macroscopic four-dimensional space-time - but filled with an "axio-dilaton field" that takes different values throughout its volume.

If I have understood correctly, the singularities I just mentioned pertain to the combination "metric + axio-dilaton". And at 33 separate locations in ${\cal M}_{\rm max}$, there is a point or a surface where this combination becomes singular in the way described, giving rise to a gauge field (or actually, an N=1 superfield) at that location.

All these gauge superfields lead separate lives - this is a type of braneworld model, where the 33 parallel "worlds" only interact gravitationally. So although that overall gauge group is big (not as big as you said - its dimension is more like $10^{3}$), in practice it's only the individual factors which are relevant, one for each braneworld.

If this does describe reality, we must be in one of the $E_8$ braneworlds.