The idea that the gauge fields of the Standard Model are extended not just to \(\NNN=1\) supersymmetry multiplets but to \(\NNN=2\) supermultiplets has been discussed a few times on this blog, e.g. in November 2011.
Those blog entries were mostly inspired by phenomenologists who had good enough low-energy if not low-brow reasons to add a chiral multiplet in the adjoint representation to the vector multiplets.
However, I always found such an extension very natural from a braneworld viewpoint. Gauge fields may reside on branes with rather high dimensions and they may preserve the \(\NNN=2\) supersymmetry while the fermion matter multiplets only respect the \(\NNN=1\) supersymmetry, being localized on intersections. This picture becomes particularly natural in F-theory, I thought, and I wondered why no string theorists discussed this scenario.
Finally, Rhys Davies, an Oxford postdoc (and infrequent physics blogger) who worked with Candelas a few years ago, published such a paper:
Dirac gauginos and unification in F-theory
He notes that the F-theory scenarios of this kind break the usual calculations suggesting the "gauge coupling unification" miracle, anyway. So it's not insane to sacrifice this old-fashioned unification by adding the new multiplets. However, he starts from scratch and tries to restore the unification.
The author concludes that with some new vector-like multiplets etc., the gauge coupling unification returns – and it occurs at the reduced Planck scale. Moreover, such a picture may become natural if the gauge fields live on a K3 cycles rather than, for example, a del Pezzo cycle which is the usual assumption in the F-theory model building.
One of the many advantages of the K3 surfaces – beyond those listed in the paper – is that I have this nice animated GIF with one of them.
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