Interesting post here http://motls.blogspot.com/2005/10/heterotic-mssm.html#comments It seems that a group of researchers has constructed a Calabi-Yau compactification that reproduces that particles of the standard model. The also obtain the SO(10) GUT group, and seem to get rid of some of it's less usefull properties (like Higgs triplets). Could this be a new boost for String Theory? I'm fairly new at all this, so any insights any of you could give would be appreciated.
It looks very interesting. They don't get the standard model per se, but rather the Minimal Supersymmetric Model (MSSM), with its SO(10) group of local internal symmetries. The standard model is not supersymmetric (except for its intrinsic BRST symmetry), and its gauge group is SU(3) X SU(2) X U(1), which is a subgroup of SO(10) and of a lot of other groups. The new model does avoid some of the nasty Higgs problems that have turned up in the MSSM, and they predict the right number of kinds of quarks. But they don't have the quark masses yet. To my mind one of their most significant assets is giving a clear explanation (apparently; I just know it through Lubos' summary) of why, in 25 years of work since Witten et al showed this kind of model was possible, there has been no realistic work like this before. There was a "hard problem" in the Calabi-Yau specification which they have now solved topologically. And I like their topology! Long exact sequences rule! This is now turning into an exciting horserace! Early favorite SS Hope, who had seemed to flag around the far turn, is now showing champion style, challenging the leaders Causal Pride and Spin Foam as we come into the stretch! And don't ignore Asymptotic Freedom making a fine run, and dark horse Son of Phoenix coming up on the outside! The stands are going wild! Cheers and trash talk fill the air!
good imagery and rings true. Motl blog attributes the development to Ovrut's team at UPenn and especially to Volker Braun. so here is the latest from Braun and Ovrut, plus a list of papers that appeared earlier this year. http://www.arxiv.org/abs/hep-th/0510142 Moduli Dependent mu-Terms in a Heterotic Standard Model Volker Braun, Yang-Hui He, Burt A. Ovrut, Tony Pantev 23 pages "In this paper, we present a formalism for computing the non-vanishing Higgs mu-terms in a heterotic standard model. This is accomplished by calculating the cubic product of the cohomology groups associated with the vector bundle moduli (phi), Higgs (H) and Higgs conjugate (Hbar) superfields. This leads to terms proportional to phi H Hbar in the low energy superpotential which, for non-zero moduli expectation values, generate moduli dependent mu-terms of the form <phi> H Hbar. It is found that these interactions are subject to two very restrictive selection rules, each arising from a Leray spectral sequence, which greatly reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We apply our formalism to a specific heterotic standard model vacuum. The non-vanishing cubic interactions phi H Hbar are explicitly computed in this context and shown to contain only four of the nineteen vector bundle moduli." 2. hep-th/0509051 Heterotic Standard Model Moduli Volker Braun, Yang-Hui He, Burt A. Ovrut, Tony Pantev 28 pages Subj-class: High Energy Physics - Theory; Algebraic Geometry 4. hep-th/0505041 Vector Bundle Extensions, Sheaf Cohomology, and the Heterotic Standard Model Volker Braun, Yang-Hui He, Burt A. Ovrut, Tony Pantev 62 pages, 2 figures 5. hep-th/0502155 A Standard Model from the E8 x E8 Heterotic Superstring Volker Braun, Yang-Hui He, Burt A. Ovrut, Tony Pantev 23 pages JHEP 0506 (2005) 039 6. hep-th/0501070 A Heterotic Standard Model Volker Braun, Yang-Hui He, Burt A. Ovrut, Tony Pantev 12 pages Phys.Lett. B618 (2005) 252-258
I think your numbers 2 and 6 concern the model in question, perhaps without the latest calculations reported by Lubos. I am going to go look at your number 4, to see if I can make sense out of their techniques. There is also a link to a paper on sheaves for physicists in Lubos' account at Dimitri's link.
thanks for reminding me about Sharpe's lectures on sheaves. here is the link: http://arxiv.org/abs/hep-th/0307245 Lectures on D-branes and Sheaves I include it simply as a library-type convenience for anyone interested---haven't looked at it. I have to go out this afternoon. Glad you are checking these references. You are cordially invited to edit the list and make more of a biblio-commentary. I am looking forward to this development changing the terms of discussion at Peter's----no hopes either way, at least for the moment, just enjoy change. If it turns out the Landscape crisis is over, then what?
This is probably a naive question but are you talking about deriving the actual masses of the three generations of quarks from string topology? Something that would predict the oddly irregular steps from down to strange to bottom (roughly a ratio of - 1/16/42), or from up to charm to top (roughly 1/600/283). I familiar with how CY spaces would have three "holes" for three generations. But is there even a broad brush understanding why the actual masses of particles should be so lacking in a regular progression? Cheers - John McCrone.
Their masses are not precise, but they do have the right number of generations and the right number of particles per generation and SOMETHING like masses of the right order. Their cohomology classes give them integer masses and they say calculation of actual masses is a task for the future. But yes, I think what they have could be described as a broad brush explanation (not that I can detail that explanation, I have only been a little way into just one of their papers).
Technically this model defers from the usual KKLT models in favor elsewhere (the usual one landscapists like). Keep in mind the main problem with this model is it leaves open the cosmological constant problem (which would have to appear somewhat unnaturally in some radiative correction tadpole diagram maybe) so its not clear if the model is physical or not. This is much more of an old fashioned Stringy model or philosophy... Get the matter spectrum first, then try to look for subtle gravity effects. I heard Volkar lecture about this, and yea a lot of this stuff goes way over my head, some of the specialists were arguing about some fine points though as I recall.
I can see that the right string symmetry with the right number of holes would give the required three generations of particles, but what physically would determine the masses? Is it some harmonic deal (like quantum levels for exact electron orbits around a proton)? Is it something to do with the way the holes in a CY realm are "spaced out"? Elsewhere Kea said "In other words, the generations are not to be thought of as different particles but as different observations of the same thing, the probability depending in some way upon scale." Does this say anything about a mechanism that would generate a seemingly pretty patternless series of particle masses?
See Marcus's post, number 4 in this thread, for their papers so far. The latest calculation was just done last weekend according to Lubos, and so it hasn't been published yet.
masses aren't easy Nobody has ever calculated any particle masses from first principles in string theory. And I don't mean calculated them and gotten them right - I mean calculated them at all. The problem is that all the observable particles have zero mass compared to the string scale. To compute masses we'd need to understand small corrections to this. Among other things, this means we'd need to know how supersymmetry is broken. And nobody knows this. So, don't hold your breath waiting for people to compute particle masses in this model. My complaint here is not just about string theory, either. Nobody has any systematic sort of understanding about how particles might get specific masses. Most of the fundamental constants of nature are particle masses... explaining even one would be a tremendous breakthrough.
Agreed. If you could derive the basis for the mass of any fundamental particle from first principles [whatever those might be], I think you would be well on your way to deriving all of them. I really don't see that happening in the near future. I allow, that at some level, certain fundamental particle masses ARE first principles. The relational aspect between particle masses might be explainable, but, at some point a certain mass is simply what it is, and defies any causal explanation. Not unlike the speed of light, it simply is what it is. Is that not the definition of a 'first principle'? We might be able to constrain the number of arbitrary values required, but never eliminate the need for at least one constant that defies explanation. As long as I'm proseletizing... the search for a TOE smacks of attempting to contrive the logical equivalent of a perpetual motion device.
This was my understanding hence I was a little surprised at comments that such calculations are underway in the paper originally cited. Nevertheless, has anyone come across even half decent speculation about why the particle masses should be so apparently random? If mass is a product of some kind of resonance, then you might expect each step up in generation to be a simple multiple. Or even if the pattern was slightly complex for some reason, perhaps because like the "spacing" of the three CY holes was irregular, then the difference between all generation two and generation three particles ought still to be the same sized step. Yet the step from down to strange quark is small compared to that from up to charm, then from strange to bottom is slightly larger than from charm to top. Is this what people would expect from analogs with other physical systems like quantum levels in electron shells? What sort of analogy should ground our thinking here?
As I understand it, mass is the only property that generates and responds to gravity. So it would seem that we are not going to understand where mass comes from until we understand gravity (spacetime) itself.
The MSSM model that this superstring model reduces to includes a Higgs sector with one extra particle-antiparticle pair. The interaction of these with the ordinary Higgs bosons could introduce some variation in the mass-conveying Higgs mechanism, but I am not up to saying how that would work. The authors are apparently working in this direction though.
Is there any form of energy not dependent on mass (not really, E=mc^2). How about the potential energy derived from the separation of electrically charge particles? As I understand it charge is derived from some sort of spacetime symmetry of the particles. And other kinds of spacetime symmetry give rise to the Strong force and the Weak force. So if symmetry gives rise to force and thus energy which is equal to mass, then is mass a measure of symmetry, or a different kind of symmetry, etc?