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March 12, 2007

The Standard Model Landscape

One of the most consistently misunderstood features to emerge from the study of string compactifications is the existence of a “landscape” of metastable vacua. Surely, it is a grave defect of the theory to possess so many solutions! Obviously, the string theorist must be on the wrong track.

But, if you think about the matter, you quickly realize that the essential ingredients: coupling to gravity, and a source of violation of the null-energy condition, are rather commonplace. Arkani-Hamed, Dubovsky, Nicolis and Villadoro have a beautiful paper, in which they point out that the requisite conditions are present in the rather minimalist context of the Standard Model, coupled to gravity, with massive neutrinos. As long as there are no other light fields1, their analysis holds for any theory containing the Standard Model, including — one hopes — string theory.

In Type II flux vacua, it is negative tension of the orientifold planes that supplies the violation of the null energy condition. In Arkani-Hamed et al’s story, it is the Casimir energy due to light fermions with periodic boundary conditions on a circle. In the simplest case, they looks at a compactification on AdS3×S 1\times S^1 with positive 4D cosmological constant. At the classical level, the potential for the “radion”, the 3D scalar governing the radius of the S 1S^1, is of a runaway form, and the solution, just described, is a funny way of writing dS4.

But the Casimir effect, for fermions with periodic boundary conditions on the S 1S^1, induce a 1-loop correction to the potential for the radion, which tends to make the circle shrink, rather than expand.

By happy coincidence, the neutrino masses in the real world are comparable in scale to the 4D cosmological constant, and can stabilize the radion at a finite radius of the S 1S^1 (of order a few microns). The 3D effective cosmological constant is negative, with the AdS3 radius somewhere on the order of the 4D Hubble length (10 25\sim 10^{25}m).

The existence of these vacua is entirely an infrared effect. The existence of more massive degrees of freedom like, say, the electron, induce only tiny corrections of order e m e/m μe^{-m_e/m_\mu}. Indeed, the smallness of these corrections means that the scalar dual to the photon in 3D has a nearly flat potential.

For all intents and purposes, particle physics in any of these vacua is the same as in our 4D world.

There is quite a fun story to do with other “compactification” geometries.

But, I think the bottom line is that we should not be particularly alarmed at the presence of a large number of vacua. Any theory worthy of our consideration will, likely, possess a similarly large number of vacua. If we should be disturbed by anything, it is that, out of the plethora of string vacua found to date, none of them looks sufficiently like our world, rather than that there are too many that do.


1 The presence of other light fields like, say, the axion, certainly affects the analysis and could upset the vacua that they found, or could create even more vacua, depending on the details.

Posted by distler at March 12, 2007 1:45 AM

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6 Comments & 0 Trackbacks

Re: The Standard Model Landscape

Jacques,

as for your comment
> If we should be disturbed by anything …

it seems to me the main issue is that we know how to fit the standard model (parameters) to experiment, but we do not have a procedure to pick the right vacuum in the string landscape to find/fit the standard model.

Maybe one day somebody will just get ‘lucky’ or find a new guiding principle somehow. Otherwise statistics (to avoid the A-word) seems the only other way forward.

Posted by: wolfgang on March 12, 2007 11:02 AM | Permalink | Reply to this

Re: The Standard Model Landscape

it seems to me the main issue is that we know how to fit the standard model (parameters) to experiment, but we do not have a procedure to pick the right vacuum in the string landscape to find/fit the standard model.

If there were any string vacua that looked (at any level detail) like the Standard Model, that might, indeed, be the “main issue.”

Maybe one day somebody will just get ‘lucky’ or find a new guiding principle somehow. Otherwise statistics (to avoid the A-word) seems the only other way forward.

Finding an appropriate vacuum is not a blind search (since we have a pretty good idea what we are looking for and what will — and will not — yield what we are after).

At present, however, we don’t have an ensemble on which to do statistics.

Posted by: Jacques Distler on March 12, 2007 11:20 AM | Permalink | PGP Sig | Reply to this

Re: The Standard Model Landscape

so what do you think about this paper?

Posted by: wolfgang on April 2, 2007 8:11 PM | Permalink | Reply to this

Re: The Standard Model Landscape

I am not sure if I understand what Arkani-Hamed, Dubovsky, Nicolis and Villadoro mean with the first sentence of their paper:

M-theory is a unique theory with a unique 11-dimensional vacuum.

I assume this is supposed to be just the argument which they make for 4d-gravity-plus-SM, now applied to 11d supergravity. Is that right?

Posted by: urs on March 13, 2007 1:46 PM | Permalink | Reply to this

11 Dimensions

The statement is a little imprecise (hinging on what is meant by the phrase “11-dimensional”). More precisely, one could say that there is a unique vacuum with unbroken 11-dimensional Poincaré invariance (ISO(10,1)ISO(10,1)), and no vacua with 11-dimensional de Sitter (SO(11,1)SO(11,1)) or anti-de Sitter (SO(10,2)SO(10,2)) invariance.

But there are plenty of (indeed, a landscape of) vacua with smaller symmetry groups.

The same is true of 4D gravity+SM, or any theory containing 4D gravity+SM.

Posted by: Jacques Distler on March 13, 2007 2:14 PM | Permalink | PGP Sig | Reply to this

Re: The Standard Model Landscape

I find the converse statement of this analysis extremely interesting.

Assume that no CFT exists with such a massively irrelevant spectrum, then by this analysis it *must* imply additional light states in the IR that conspire to destroy the minima in the Radeon potential.

Interesting phenomenolgy possibilities there.

Posted by: Haelfix on March 17, 2007 4:22 AM | Permalink | Reply to this

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