5.2.4 Phenomenology

There are no open strings in IIA, IIB in perturbation theory around the vacuum.

\noindent Type II does include open strings. However, they don’t show up in the vacuum perturbation theory, they are only there in connection with non-perturbative effects like D-branes.

\subsection{Classical} ^[1] \subsection{Quantize} \subsection{Type II string theories} \subsection{Type I string theory} \subsection{Heterotic string theories} \subsubsection{$SO(32)$ and $E_8\times E_8$} \subsubsection{Toroidal compactifications} \subsubsection{$\mathcal{N}=2$} ^[2] and Appendix of 7th chapter in ^[3].

\subsection{Vertex operators} \subsection{Scattering amplitudes} \subsubsection{Tree-level amplitudes} \subsubsection{One-loop amplitudes} \subsubsection{UV finiteness} ^[4] \subsubsection{$l_s\to0$ $l_s\to\infty$ \& $g_s\to 0$ limits}

\begin{outline}[enumerate] \1 Supergravity limit ($l_s\to0$): ^[5]^[6] \1 Higher spin limit ($l_s\to\infty$): \1 Free quantum string limit ($g_s\to 0$): Only tree level. \1 Classical interacting limit ($\hbar\to0$): \end{outline}

\subsection{String dualities} \subsubsection{T-duality} \paragraph{Double field theory}~
^[7] \subsubsection{S-duality} \subsubsection{U-duality} ^[8] \subsubsection{F-theory} ^[9]

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