There is some statement learnt from this paper Tumbling gauge theories by [Raby, Dimopoulos, Susskind (1979)]:

Given 4d SU(5) gauge theory with fermions in the representation $$\bar 5\oplus 10$$

Add a scalar field in $5$ with a Yukawa coupling to two of fermions in $10$ and $10$. For an appropriate potential it condenses, Higgses
$$SU(5) \to SU(4)$$
and gives masses to some of the fermions.
We have left with $SU(4)$ with fermions in
$$
1 \oplus 4 \oplus \bar{4}
$$
Standard 4d dynamics leaves a single massless fermion with the quantum numbers of a product of three microscopic fermions
$$
\bar 5 \cdot \bar 5 \cdot 10.
$$
One can read the summary of statement in p.16 of this slide

questions:

Higgses
$SU(5) \to SU(4)$ is the process of condensing $5$ by a Higgs potential, yes? I am not sure how does it give masses to some of the fermionsto be left with $SU(4)$ with fermions in
$
1 \oplus 4 \oplus \bar{4}
$? This means out of 15 fermions there are only 9 fermions left to be massless? How come only 9 fermions left not 10 (or other number) fermions?

"Standard 4d dynamics leaves a single massless fermion with the quantum numbers of a product of three microscopic fermions
$
\bar 5 \cdot \bar 5 \cdot 10.
$" But there were 9 fermions in
$
1 \oplus 4 \oplus \bar{4}
$,
is that true that both $4 \oplus \bar{4}$ are massive due to the $SU(4)$ gauge confinement dynamics? While the $1$ is the only remained massless fermion?

But the $1$ if it is the only remained massless fermion, should it be precisely from one of the 15 out of $\bar 5\oplus 10$? Then **how come it is also a composite bound state out of**
$$
\bar 5 \cdot \bar 5 \cdot 10 =(\bar 10+\bar 15) \cdot 10 = 1+ \dots?
$$
It looks that the way to get the composite bound state still not clear...?

This post imported from StackExchange Physics at 2020-11-30 18:56 (UTC), posted by SE-user annie marie heart