Lost in Translation

MSSM-like from string

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. 

Destablization

This is a talk given by Jon right before Thanksgiving. 

he and Adam Falk’s work is about one soft breaking term that people previously thought may appear in supersymmetry breaking lagrangian. They study from spontonously breaking way, found goldstino loop always appear along with this soft breaking term, just as pion decay term always appear with mass term(Goldberger-Treiman relation). Thus, if you don’t suppress the breaking term by suitable power counting factor(after that it will become small), the goldstino loop will destablize your vacuum.

Cool job.

Draft

Today, Gritsan mentioned how to calculate distance defletion inside detector — chop it into slabs.

This idea is exactly as the way Lorentz got the formula connecting reflection index and scattering amplitude, which further helped Krammers and Kronig got optical theorem.
Optical Theorem connects two things, total cross section, and forward scattering amplitude. Rediculous at the first sight, it is incredible as you give a second thought. Let us have a close view at what happened between Lorentz and K&K. The earlier person got a macroscopic quantity, reflection index, as an expression of a microscopic quantity, scattering amplitude. The story is pretty similar to atomic hyperthesis and classic theromal dynamics. Just because nature is it, no deeper reason. However, K&K reconsider a more macroscopic quantity, intensity from a more macroscopic varible, total cross section. The formula become so straightforward that once you wrote it down, everything just show up in the exact place you want. Then, they require these two to be the same, bam! optical theorm.

A second way to do it is drawing Feymann diagram, you will soon notice you are doing something stupid —- you forgot the simplest case! Write it down, read it, you got optical theorm. 

Lecture Notes 1 (9.22)

从非相对论量子力学到相对论量子场论。

motivation:
QFT内含的对称性使得公式表述异常简单，却因存在太多的纵横联系使最简明的物理思想掩盖在华丽外壳之下。既然量子力学作为QFT的极限，后者最简明的思想应该多半显示出来，事实正是如此。

Example:
1。量子力学隐含了镜像反演平方为正负1的事实，并在自由度高于2维将符号赋予玻色，费米（子）
2。非相对论玻色弦振动要求负能量激发态的反粒子解释，并在此解释下自洽。
3。非相对论费米弦振动负能量激发态不仅要求反粒子解释，还要求处理正负频对应，否则中性粒子的实条件不能满足。

homework:
将以上内容推广到高维和相对论情形，注意对称性衍生出的表述简洁，因果律在对称性联系下自然满足。
这揭示了一个事实：离散对称，初条件+连续对称=物理。

bonus:
旋量也许是低维几何最深刻的基础