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Some additions on cosmology

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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
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Riccardo
2020-10-04 12:09:49 +02:00
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sec/part1/introduction.tex
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@@ -1308,12 +1308,12 @@ These stacks would separately lead to a $\U{3} \times \U{2}$ gauge theory.
It would however be theory of pure force, without matter content.
Moreover we should also worry about the extra \U{1} groups appearing: these need careful consideration but go beyond the necessary analysis for what follows.
Matter fields are notoriously fermions transforming in the bi-fundamental representation $(\vb{N}, \vb{M})$ of the \sm gauge group~\eqref{eq:intro:smgroup}.
For example left handed quarks in the \sm transform under the $(\vb{3}, \vb{2})$ representation of the group $\SU{3}_C \otimes \SU{2}_L$.
Matter fields are notoriously fermions transforming in the bi-fundamental representation $(\vec{N}, \vec{M})$ of the \sm gauge group~\eqref{eq:intro:smgroup}.
For example left handed quarks in the \sm transform under the $(\vec{3}, \vec{2})$ representation of the group $\SU{3}_C \otimes \SU{2}_L$.
This is realised in string theory by a string stretched across two stacks of $3$ and $2$ D-branes as in the right of~\Cref{fig:dbranes:chanpaton}.
The fermion would then be characterised by the charge under the gauge bosons living on the D-branes.
The corresponding anti-particle would then simply be a string oriented in the opposite direction.
Things get complicated when introducing also left handed leptons transforming in the $(\vb{1}, \vb{2})$ representation: they cannot have endpoints on the same stack of D-branes as quarks since they do not have colour charge.
Things get complicated when introducing also left handed leptons transforming in the $(\vec{1}, \vec{2})$ representation: they cannot have endpoints on the same stack of D-branes as quarks since they do not have colour charge.
We therefore need to introduce more D-branes to account for all the possible combinations.
An additional issue comes from the requirement of chirality.
@@ -1338,7 +1338,7 @@ The light spectrum is thus composed of the desired matter content alongside with
\end{figure}
It is therefore possible to recover a \sm-like construction using multiple D-branes at angles as in~\Cref{fig:dbranes:smbranes}, where the angles have been drawn perpendicular but can in principle be arbitrary~\cite{Ibanez:2001:GettingJustStandard,Grimm:2005:EffectiveActionType,Sheikh-Jabbari:1998:ClassificationDifferentBranes,Berkooz:1996:BranesIntersectingAngles}.
For instance quarks are localised at the intersection of the \emph{baryonic} stack of D-branes, yielding the colour symmetry generators, with the \emph{left} and \emph{right} stacks, leading to the $( \vb{3}, \vb{2} )$ and $( \vb{3}, \vb{1})$ representations.
For instance quarks are localised at the intersection of the \emph{baryonic} stack of D-branes, yielding the colour symmetry generators, with the \emph{left} and \emph{right} stacks, leading to the $( \vec{3}, \vec{2} )$ and $( \vec{3}, \vec{1})$ representations.
The same applies to leptons created by strings attached to the \emph{leptonic} stack.
Combinations of the additional \U{1} factors in the resulting gauge group finally lead to the definition of the hypercharge $Y$.