String Theory Taxonomy, Musing On SUSY and Neutrino Condensates

String Theory Taxonomy

Lubos has a helpful and somewhat lengthy taxonomy of the main subtypes of string theories, explaining in broad general terms how they can be seen as manifestations of the same thing and which of the various types are most attractive to fit to the Standard Model and General Relativity, although even his explanation is a bit heavy on abstract algebra jargon and topology jargon for the average lay reader.

Ultimately, the bottom line points are that string theory versions that make any sense imply some sort of maximal supersymmetry with supergravity as an approximation in reasonably observable situations.

General Observations About String Theory

My gut instinct is to ask myself is one really needs a 10-11 dimensional manifold with six or seven compactified dimensions and a group theory that predicts twice as many particles as we've ever had any experimental indication actually exist, sometimes with more bells and whistles to replicate the Standard Model in four dimensions and four dimensional relativity with ten element tensors that capture all of the different ways that a point in a mass-energy field may acquire mass-energy from non-gravitational sources.

Sting theory introduces a lot of subtle moving parts that may not have any obvious experimental justification. The elaborate topologies needs to make all those dimensions work in anything approaching a real world scenario are anything but natural.

Also, after a while, it becomes clear that the main impetus for the very elaborate many dimensional space-time structure that string theory proposes is basically to make gravity, which typically operates in the whole of this elaborate space-time, weak relative to other Standard Model forces.

String theory also seems to unduly reify the stress-energy tensor of general relativity, which is really just an algebric accounting tool for keeping track of all of the mass and energy contributions to gravity at a point and then have gravity respond to the type of these mass-energy contributions as well as their absolute value. Space-time in general relavity twists and turns like the matter-energy fluxuations that give rise to it, rather than simply attracting with a scalar field proportional to the absolute value of the mass-energy stuff at a point as Newtonian gravity does. But, it seems like we ought to be looking for a model in Einsteinan four dimensional space (which due to special relativistic boost factors of momentum are represented as three dimensions of their own in general relativity) that recognizes that all the elements of the stress-energy tensor flow out of different actions in four dimensional space, rather than arbitrarily compactifying them.

Surely there must be some way to simply state a general relativistically consistent variation in the Standard Model to embed in ordinary four dimensional General Relativity, perhaps formulated in a more parallel way, since many string theories seem to find the Standard Model portion of the theory to a four dimensional brane or manifold or extended set of dimensions that it can't depart from anyway.

In other words, while String Theory is attractive largely as a means to unify fundamental physics, the glue holding the parts together seems to show if you look closely anyway, in addition to predicting esoterica that we don't see and not predicting anything new that we do see.

String Theory Is Fundamentally A Generalization Of SUSY

It simply isn't obvious to me that we need to resort to SU(32) Lie algebras and groups in eleven dimensions in order to figure out how the Standard Model and/or General Relativity need to be reformulated to make the theory consistent.

I suspect that the problems with the Standard Model which String theory solves with Supersymmetry have another solution that it different in kind and flows from some subtle point in the Standard Model that is not quite right the way that we have proceeded so far.

We've probably got something not quite right in our equations or the way that we are manipulating them that makes terms that actually cancel out seem like they don't because they are mere close approximations that don't hold to far from the numerical values of the formulas that they were derived from in the first place.

Put another way, historically supersymmetry came first, and string theory was invented to reveal deeper connections and implications resting in SUSY, which is all good and well if SUSY is solving the problems of the Standard Model in the right way. But, a theory of everything built to integrate SUSY with General Relativity makes no sense if SUSY is the wrong solution to the problems with the Standard Model that it addresses.

Why SUSY (Or Technicolor)?

What are those motivations for SUSY?

In a nutshell, per Wikipedia:

It is motivated by possible solutions to several theoretical problems. . . .

If supersymmetry exists close to the TeV energy scale, it allows for a solution of the hierarchy problem of the Standard Model, i.e., the fact that the Higgs boson mass is subject to quantum corrections which — barring extremely fine-tuned cancellations among independent contributions — would make it so large as to undermine the internal consistency of the theory. . . . Other attractive features of TeV-scale supersymmetry are the fact that it allows for the high-energy unification of the weak interactions, the strong interactions and electromagnetism, and the fact that it provides a candidate for Dark Matter and a natural mechanism for electroweak symmetry breaking. . . . Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the Coleman–Mandula theorem, which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories like the Standard Model under very general assumptions. . . . In general, supersymmetric quantum field theory is often much easier to work with, as many more problems become exactly solvable.

Technicolor too (at this point "walking technicolor" since trival versions of the theory have been ruled out by experiment) seems to be trying to solve the same problems as SUSY rather than considering that the problems themselves may be artificial consequences of a not quite right formulation of the forces and mass generation mechanisms whose apparent flaws it is motivated to resolve.

Reasons To Doubt SUSY and Technicolor

But for the TeV scale pathologies of the Standard Model equations as currently formulated, nobody would consider SUSY or Technicolor and we would be left with a far less elaborate theory to figure out how to embed in general relativistic gravity.

Some of these theoretical motivations are looking increasingly less convincing.

Warm dark matter theory which appears to work better than cold dark matter calls for a dark matter candidate with properties, like a keV scale mass that supersymmetry does not naturally provide. The LENS experiment that is in the process of being set up is designed to directly detect dark matter if it is in this mass range (perhaps, for example, as a composite particle made up of neutrinos).

The high energy unification of the three forces of the Standard Model may be a category error (i.e. the three forces may not operate at energy ranges great enough to allow them to converge) or may be a product of something as subtle and technical as the proper non-linear formulation of one or more of the three beta functions that describes how those constants run with energy.

Our difficulty in solving the existing equations may mean that we lack a helpful component in our mathematical tool kit to work with the equations that we have, rather than that the Standard Model is fundamentally flawed. Some mathematician may come up with the next Fourier transform or Laplacian equation or Hamiltonian or finite formula equivalent to some class of infinite series, and with this one new trick we may be able to calculate with these equations much better.

After all, we've seen this happen before. The practical possibility of using QED and the unified electroweak force equations relies heavily on the mathematical trick of renormalization, which Feynman, one of its creators, believed to his deathbed contained some subtle lack of rigor that made it not perfectly valid. If some mathematician could figure out in what way renormalization was not rigorous and slightly tweak it to resolve that issue, our calculation problems and TeV instabilities might be promptly resolved and the new formulation of the renormalization process might even provide us with some deeper insights. This is not necessarily a hopeless effort.

For example, numerical approximations have confirmed in the last few years that a non-perturbative solution to the QED equations does not contain the Landau pole the appears at very high energies in the ordinary renormalized calculations. See, e.g. here ("In the case of the asymptotic behavior β(g) ~ g, the Landau pole is absent and internal limitations on the applicability of the Standard Model implied in this estimate really do not exist.") and here.

The fine tuning of the Higgs boson mass that is present in the current equations may be because we have the wrong formula for calculating it (which we haven't observed yet), or because the Higgs mechanism is not how mass is generated, not because it lacks supersymmetric particles.

LHC experiments have put increasingly high minimum mass limits on particles predicted by SUSY and Technicolor, which pushes these theories into less natural parameter spaces.

My suspicion is that a lot of the pathologies that SUSY and Technicolor are trying to solve, fundamentally, have something to do with the formulation of the Standard Model, or perhaps the formulation of General Relativity, not being quite right in a way that has few phenomenological implications in practical settings but has theoretical rigor issues that prevent an elegant unification.

For example, it may very well be that there is a non-perturbative way to do QED without renormalization that we have not yet discovered that rids it of its theoretical pathologies and insecurities and also happens to be more easily formulated in a general relativistic rather than Minkowski special relativistic background.

Doubling the number of particles and adding a large number of free parameters to those found in the Standard Model seems like a very high price to pay to get an afterthought method for generating particle mass whose formula could be not quite right to balance properly and to break an electroweak symmetry that is put into their unification "by hand" in a not entirely elegant or natural formulation in the first place. Maybe electromagnetism and the weak force shouldn't be unified at all and it is merely possible to do so because of some similarity of all three forces understood at a deeper level.

What The Loop Quantum Gravity Program May Reveal

Attempts to embed the Standard Model into loop quantum gravity, which is an emergently four dimensional space-time background, looks like more fruitful avenue to explore than String Theory.

It could be that space-time really is analog rather than digital and that it is actually wrong. But, even if space-time is continous rather than discrete, if loop quantum gravity motivates even a non-unified discrete variant of general relativity space-time consistent formulation of the Standard Model, that formulation of the Standard Model may make clear in what ways some or the other parts of the existing Standard Model formulation are flawed, and the reformulated new and improved formulation that is consistent with General Relativity in the first place may be easier to unify into a grand unified theory.

Resolving these subtle issues may also resolve existing issues in the Standard Model which leave too many unexplained coincidences and question marks, like the almost pattern fitting mass matrix, the not quite coinciding running gauge coupling constants of the three Standard Model forces, quark-lepton complementarity, the prospect of unpredictable high energy electroweak behavior due to theoretical instabilities, and the unexpectedly small number of parameters needed to specify the CKM and PMNS matrixes.

In other words, we should fix the theoretical pathologies in the Standard Model to the extent possible before we try to embark on grand unification or a theory of everything, and the loop quantum gravity program seems to be advancing the cause of fixing those pathologies.

We Don't Understand Mass Well

Let's face it. We really don't understand the source of mass in the Standard Model well at all.

We are just beginning to come to terms with the way in which the Yang-Mills equation for QCD turns bare quarks and gluons, components that individually have almost no mass, into protons and neutrons and other hadrons in which the interactions give rise to something like 90% to 99% of the baryonic mass in the universe. But, we are almost certain that it arised from the QCD equations, not primarily from a Higgs mechanism. A similar mechanism for mass generation in neutrinos that might be superluminal was explored in an October 2010 paper.

We don't have a good explanation for the reality that all weak force interacting particles have mass while all particles that don't interact through the weak force lack mass.

We can't explain why the fermions of the Standard Model show the mass relationships to each other that they do, despite the fact that there is clearly some sort of pattern involved and we can even use Koide's formula to show what appears to be an exact theoretical relationship between the three charge lepton masses.

There is a striking apparent connection between the Einstein-Hilbert general relativity equations in certain formulations and a certain formulation of the square of a Yang-Mills equation that seems to parallel seeming relationships between the square root of the fermion mass matrix and the CKM and PMNS matrixes.

We can't definitely resolve the question of whether dark matter effects arise from the highly predictive modified gravity theories, or from warm dark matter particles of keV masses with neutrino-like properties that aren't a match to any theoretically and experimentally well supported particle from high energy physics (new experimental evidence strongly disfavors the traditional cold dark matter theory relative to either of the other options). Likewise, there is more than one mechanism that can explain dark energy.

New Neutrino Physics Discoveries

We just discovered pretty definively that the neutrino has mass. We are still working hard to determine if neutrinos acquire mass by a different mechanism than the Higgs mechanism we've tried to use to explain it in other fermions. We have also determined, as one would expect in a massive neutrino scenario, that there are probably at least three different masses for each of three generations of neutrinos. But some of our data show closer fits to there being four or five experimentally detectable neutrino types which is not a good fit to the canonical "periodic table" of fundamental fermions at all. Even problems deeply intertwined with mass in general relativity and special relativity, like the speed of light relative to the maximum speed of a massive neutrino, have suddenly started looking like islands of mystery instead of the settled points of certainty that they seemed to be just a year ago.

All of these new developments in neutrino physics within the last few years create new problems for the Standard Model that make the aesthetic problems that motivate SUSY look trivial. Most of these new developments are deeply intertwined with what we don't understand about mass generation in the Standard Model and the Higgs mechanism as currently formulated in the Standard Model doesn't really squarely address these questions.

Saving Physics With Neutrino Condensates

One suggestion for several of the problems that are addressed by SUSY and Technicolor, is that the much sought after Higgs boson, electroweak symmetry breaking, and perhaps dark matter as well, can be described by adding right handed neutrinos to the Standard Model and assuming composite mass entities made up of neutrinos in a superfluid state called a neutrino condensate. Adding right handed neutrinos to the Standard Model is a well motivated extension of it that does little to upset its basic structure, although we have yet to see any hard evidence that even these exist and condensed matter physics provides ample tools to analyze these states.

It might even be possible for these condensates to arise due to ordinary gravity. Neutrino condensate theory also suggests that neutrinos may uniquely lead to Lorentz symmetry violations. It has even been suggested that even that gravity itself could arise from weak force interactions of relic neutrino condensates left over after the Big Bang that also dynamically give rise to gravitons as Goldstone bosons. Versatile creatures that neutrino condensates are, they can also be used to explain dark energy and the Hubble constant from first principles, or provide a cause for cosmological inflation and explain why we have more matter than antimatter in the universe. Neutrino condensates could also help explain the internal workings of neutron stars, neutral kaon decays, and top quark decays.

Some of the neutrino condensate predictions associated with these theories might be possible to examine experimentally with precisely measurements of low energy beta decays and in neutron star behavior. While hardly cheap, either kind of experiment would probably be much less expensive to build and operate than a successor to the LHC. Like efforts to observe neutrinoless double beta decay in radioactive elements, this is medium budget physics instead of big budget physics.

My point is not necessarily to actually argue that neutrino condensates are the answer to every unsolved physics question out there. Instead, it is to illustrate that it is conceptually possible for a relatively minor tweak to the Standard Model (adding just three fermions that already seem to be "missing" in the current fundamental fermion chart and possibly no new fundamental bosons, although some versions of these theories do require a new neutrino specific interaction), when supported by a bit of analysis based on existing facts we know about condensed matter physics, could conceiveably solve the Standard Model pathologies that motivated SUSY in a far more parsimonious manner.

Even if neutrino condensates are experimentally proven not to exist or have the effects predicted, the fact that a tweak of this kind could solve many Standard Model pathologies suggests that physicists who limit their set of potential solutions to them to variants on SUSY and Technicolor have their blinders on too tightly and need to be more open to other potential remedies to these issues.