Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

February 7, 2003

Heterotic Nostalgia

(Yup, another MathML-enabled post. The usual caveats apply: you need the fonts and you need Mozilla to see the equations as they were intended.)

I gave a talk today in our Brown bag seminar about doublet-triplet splitting (and related matters) in String/M-Theory. It made me feel old because most of the audience were far too young (having been in elementary school at the time) to be familiar with the heterotic version of the story. But it also made me realize what had been (to me, at least) a nagging lack in the M-theory version of the story, as promulgated to date.

One of the great successes of the heterotic story was that one obtains the “successful” predictions of SU(5) SUSY GUTS (e. g. for sin 2 (θ W) ), without some of the less-successful features (the doublet-triplet splitting problem, SU(5) relations among superpotential couplings, … ).

The origin of this is that, in the heterotic string, unlike in conventional GUTS, the generations do not form SU(5) multiplets. The vertex operators for quarks and leptons in a single “generation” are constructed using distinct chiral primaries of the internal SCFT. If there’s just a single 5 +5 of Higgses, the corresponding chiral primaries must be invariant under the n orbifolding. Hence they don’t give rise to massless colour triplets*.

This feature of the heterotic story has, so far, been invisible in the M-theory approach. I strongly believe (at least in some cases) that it is still there, but it is a bit harder to tease out of the M-theory formulation.

* If people are curious to see the details, I could put up some TeXed notes on the subject. I can’t be bothered to do it in itex.

Posted by distler at February 7, 2003 10:53 AM

TrackBack URL for this Entry:   https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/92

0 Comments & 0 Trackbacks

Post a New Comment