# Breaking of E6 to SO(10) in heterotic string theory

+ 6 like - 0 dislike
35 views

Some of the heterotic string models have an $E_6\otimes E_8$ symmetry. Examples include some orbifold models, some free fermionic models and Gepner models. We can break the gauge symmetry by including Wilson lines. Does anyone know if it is possible to break $E_6$ to $SO(10)$ while maintaining spacetime SUSY? I have seen examples in Gepner models where $E_6$ is broken to a smaller group than $SO(10)$ while keeping SUSY but none where $E_6$ is broken to $SO(10)$. Is this pure coincidence or is there a reason behind it? Any insights are appreciated!

This post imported from StackExchange Physics at 2014-03-31 16:00 (UCT), posted by SE-user Heterotic

edited Apr 19, 2014
Try the keyword NAHE. See for instance this paper

This post imported from StackExchange Physics at 2014-03-31 16:00 (UCT), posted by SE-user Trimok

+ 1 like - 0 dislike

I thought I might write an update on this in case anyone else is interested...

The answer is yes, we can break $E_6$ (to anything) while maintaining spacetime SUSY. Models with $E_6$ are known as $(2,2)$ and models without $E_6$ as $(0,2)$. $(0,2)$ means N=0 Superconformal symmetry on the the left-moving sector on the worldsheet and N=2 Superconformal symmetry on the right-moving sector on the worldsheet. There is a big literature on $(0,2)$ models but the important information is that they do indeed have spacetime SUSY. In fact, a theorem in this paper states that $N=1$ spacetime SUSY requires (at least) $(0,2)$ worldsheet SUSY.

The take home message is that $E_6$ gauge symmetry on the bosonic sector corresponds to N=2 Superconformal symmetry on the worldsheet.

This post imported from StackExchange Physics at 2014-03-31 16:00 (UCT), posted by SE-user Heterotic
answered Dec 30, 2013 by (525 points)

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysi$\varnothing$sOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.