Friday, July 25, 2014

Realistic heterotic non-supersymmetric models

Michael Blaszczyk (we will ultimately teach them to write it as "Blaščik" as any other decent non-Eastern Slavic nation) and three co-authors from German, Greek, and Mexican institutions wrote an interesting paper
Non-supersymmetric heterotic model building
where they show how naturally the \(SO(16)\times SO(16)\) heterotic string theory without supersymmetry is able to produce unifying models with one Higgs doublet, three generations, some logic inherited from non-supersymmetric \(SO(10)\) grand unified theories, and (almost?) nothing beyond the Standard Model at low energies.

Note that the \(SO(16)\times SO(16)\) heterotic strings treats the projections and sectors for the extra world sheet fermions (or bosons) a bit differently. Effectively, one changes the statistics of the \({\bf 128}\) chiral spinor of the \(SO(16)\) groups to the opposite statistics which splits the \({\bf 248}\)-dimensional multiplets of \(E_8\) back to \({\bf 120}\oplus{\bf 128}\), breaks both \(E_8\) groups to \(SO(16)\), and breaks supersymmetry.

Non-supersymmetric string theories generally have tachyons. However, they show that at smooth Calabi-Yaus – Calabi-Yau manifolds are not really that special once you break spacetime SUSY (they chose them for simplicity, to use the existing tools) – the non-supersymmetric heterotic string theory doesn't really have any tachyons. So if such tachyons appear in twisted sectors near orbifold points, and they do, they must become massive and harmless if the orbifold singularity is resolved.

With low-energy supersymmetry, one of course sacrifices certain things like the "solution of the hierarchy problem" – which doesn't seem to be a big sacrifice based on the null results that keep on flowing from the LHC.

Conceptually, I would say that these non-supersymmetric heterotic models still belong to a supersymmetric theory. Just the SUSY is broken at the string scale, not at low energies. The non-supersymmetric 10D string theories may be related to the supersymmetric 10D stringy vacua by various T-dualities etc. so they must also be understood as solutions to the same a priori supersymmetric theory – the SUSY breaking may always be understood as a spontaneous one.

Even with these non-SUSY models, it's remarkable to see how "directly" string theory produces a Standard Model. The standard embedding really seems to be "pretty much exactly what we need" to get the Standard Model spectrum.


  1. Are you suggesting that Poles aren't a decent nation?

  2. What I wrote, semi-seriously, is that they are not a decent Western Slavic nation when it comes to their spelling of the consonants.

  3. What is your opinion on the universe being a black hole in a 5D brane in Unscientific America?

  4. I have Poles and Hungarians among my ancestors so I'm genetically predisposed to like digraphs, and trigraphs too (like Polish 'dzi' or Hungarian 'dzs'). I'm aware of the fact that Poles feel some kind of affection towards Czechs but I'm also sure that they wouldn't tolerate any attempt to change their alphabet even if it would make them more close to Czechs or more slavic in general. Over the centuries Poles were having much better relations with non-slavic nations like Hungarians, Lithuanians, Swedes or even some groups of Tatars than other Slavs, so I wouldn't be surprised if they preferred to use their digraphs instead of carons, only as a symbol of independence and defiance against Pan-Slavism;)

  5. But you realize that Czech spelling of the surname makes it sound totally different than original Polish one?

    It's probably cool paper, but I don't understand much of it except some algebra part. But from what i see, this paper is rather a sketch than some complete proposal. Anyways, it seams like cool project.

  6. Hmm, I think that the idea that the Poles feel closer to the Hungarians or even Tatars than us today is an amusing historically based science-fiction. No poll indicates anything of the sort, to say the least.

    We're not any kind of "obedient pan-Slavs", either, as you know very well.

    Our alphabet with diacritical signs wasn't introduced by Jan Huss in order to be pan-Slavic. It was introduced because it is far more efficient and logical.

  7. Well, yes, I do realize that, and while it's possible that the Poles will only fix their spelling, I would indeed advise them to fix the pronunciation, too - two fixes at one time wouldn't be bad. ;-)