13.10 Little string theory

\section{Twistor theory} ^[1]^[2] see also section TwistorString. \subsection{Real slices and reality structures} \subsection{$\mathbb{M}_{\mathbb{C}}$’s conformal structure $=\mathbb{PT}$’s complex structure} \subsection{Penrose transform} \subsection{Gauge theory} \subsection{Ambitwistors and $d>4$} ^[3] \subsection{Mini-Twistor theory} ^[4] \subsection{Miscellaneous} ^[5] \section{Canonical quantum gravity} ^[6] \subsection{ADM formalism} ^[7] \subsection{Wheeler–DeWitt equation} \section{Loop quantum gravity} ^[8]. For criticism see ^[9]. \subsection{Ashtekar variables} \subsection{Quantum Riemannian geometry} \subsection{Spin foams} ^[10] \subsection{Black hole entropy} ^[11] \subsection{Loop quantum cosmology} ^[12] \section{Asymptotic safety} ^[13]. It is also called nonperturbative renormalizability. For criticism see ^[14].

\setlength{\epigraphwidth}{.88\textwidth} \epigraph{Well, I think it’s yielding very useful insights. And um, I think it’s… it’s been disappointing because the idea of string theory as a theory of fundamental forces has been around now for quite a while, uh, a number of decades, and it has not led to the kind of specific prediction. Well, it makes some qualitative predictions, like it explains why gravity has to exist, but it has not led to the kind of specific numerical predictions, which will say, well, okay, now you can take it to the bank. Um, But it’s the only game in town. Um, there are alternatives for pictures of what happens at very short distances. There’s one due to me called “asymptotic safety” which I… I think is a possibility worth taking seriously, but is much less attractive than the string theory and um, I hope string theory is right, but and I don’t see anything else on the horizon that’s remotely as attractive. Andy, do you agree with that?}{Steven Weinberg [\href{https://www.youtube.com/watch?v=PFJ46G8BflQ&t=3108s}{URL}]}

\setlength{\epigraphwidth}{.88\textwidth} \epigraph{But even so, I find string theory very attractive and if I had to bet my life I would bet on string theory rather than on asymptotic safety.}{Steven Weinberg ^[15]}

\section{Hořava–Lifshitz gravity} ^[16]

\section{Causal set theory} ^[17] \section{Causal fermion systems} ^[18]

\section{Causal dynamical triangulation} ^[19] and ^[20] discuss decretized 1D quantum gravity in this approach. Regge calculus ^[21] was the predecessor to CDT. \section{Group field theory} ^[22] \section{Unimodular gravity} ^[23] \section{Massive gravity} ^[24]

\pagebreak

\appendix \section{Miscellaneous math}

\pagebreak

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\acknowledgments \addcontentsline{toc}{section}{Acknowledgements}

I acknowledge that life is meaningless. I thank the fundamental laws of physics for being mathematically comprehensible and mysterious, but I will not thank the laws of physics for being amoral and absurdly pointless.

\setlength{\epigraphwidth}{1\textwidth} \epigraph{How strange is the lot of us mortals! Each of us is here for a brief sojourn; for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people — first of all for those upon whose smiles and well-being our own happiness is wholly dependent, and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving….}{Albert Einstein (1931)}

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