Akin Wingerter’s talk today is about building MSSM-like model from string compactification.

Gauge hierarchy and family structure of fermions confused a whole generation of people. We are so eager to have a more fundanmental(or upper) understanding that we counldn’t help building all possible toy model based on imagenation. People like this can get jobs simply because, a real “top-down” touch is just impossible. Roughly speaking, everything can happen.

Akin Wingerter and cooperation tried a hybrid way: they guess a semi-completion from low energy Standard Model(SM), then scan all possible true UV completion a.k.a. string theory, based on rules obtain from SM requirement.

The GUT scale model they considered is a 6-d with 4-d flat while other 2 compactified into torus adding Z2 symmetry(so called orbitfold). The gauge field is SO(10) inside bulk and SU(5), SU(4)XSU(2)XSU(2) etc on the fixed point. The real world people living in 4-d observe an intersection which is SU(3)XSU(2)XU(1) SM gauge.

A good news is the solutions are usually rare. For instance, in heterotic string case, using a generic form superpotential, they found number of solutions as 15.

The first bad news is a technical one, you may run into wrong Yukawa matrices. It may not be a real problem, for higher order operators can be added. Except for that, fermion mass hierarchy can be explained by string instanton, location in extra dimension or whatever your favorite in string theory, while VEV of moduli over compactification scale buy you more suppression factor.

A real bad news is proton decay. The reason is simple: no one so far know how to build a non-susy domain wall, thus they require a GUT susy. The consequence is the exsitance of power 5 operator which cause proton decay fastly. Another problem is SUSY breaking now may lack messenger sector.

I think this work is pretty good. We don’t know whether the true world is reduced from a heterotic string or a type-II one. We don’t know whether there exists non-susy orbitfold either. The only way to get an answer is to try hard. Their work shed a light on how to try. And string theorist will be happy, for their work could be linked to our real life, maybe not now, maybe in a complicated way.