12.1 Off-shell string theory

\subsection{Black holes} ^[1] \subsubsection{Statistical origin of the entropy} \subsubsection{Wormholes} \paragraph{Wormholes in the axiverse}~
^[2] \subsubsection{Fuzzballs} ^[3]^[4] \subsection{Chern-Simons theories} ^[5] and also sections superconformalChernSimons and Knot. \subsubsection{Quantum Gravity in 2+1 Dimensions} ^[6]

\subsection{Topological string theory} ^[7]

\subsubsection{Twistor string theory} ^[8] see section Twistor before this.

\subsection{More on scattering amplitudes} ^[9] \subsubsection{Amplituhedron} ^[10] \subsubsection{Double copy} ^[11] \subsection{Generalized symmetries} ^[12] \subsection{Pure spinor formalism} ^[13] and ^[14] for applications to AdS/CFT. \subsection{Nonrelativistic string theory} ^[15] and also nonrelativisticAdSCFT. \subsection{ $2D$ theories} JT gravity is in section JT. \subsubsection{ $2D$ string theory} ^[16].

\subsubsection{Liouville theory} ^[17] and ^[18]

\subsubsection{CGHS gravity} ^[19]

\subsection{ QCD Strings and Effective String Theories} ^[20] \subsection{ Little string theory} ^[21]

\subsection{Higher spin theory (tensionless limit)} ^[22]. See also HigherSpinHolography. \subsection{ Other proposals for quantum spacetime} Section NG covers noncommutative geometry, which is the most promising candidate for quantum spacetime within string theory. Here, we will discuss alternative quantum spacetime proposals inspired by string theory. \subsubsection{Stringy differential geometry} ^[23] \subsubsection{Modular spacetime and metastring theory} ^[24]

\subsubsection{Generalised (Riemannian) geometry} ^[25] \subsubsection{Generalised Cartan Geometry} ^[26]

\subsection{ Open problems in string theory} Below are some important open problems within string theory. See section Problems for more broadly about quantum gravity.

What is the precise definition of M-theory or non-perturbative string theory? Will it have the following expected properties? 1) For weak string coupling, it should reduce to perturbative string theories 2) It is manifestly background-independent 3) Its structure is unique and rigid with no possibility to modify
For specific AdS compactifications, will the above definition reduce to the non-perturbative definitions given by AdS/CFT, thereby proving AdS/CFT? Can that proof be generalized to spacetimes that aren’t asymptotically AdS?
Finding de Sitter vacua and top-down de Sitter holography or proving that de Sitter is inconsistent with string theory.
Making concrete, testable predictions related to either particle phenomenology or cosmology.
What is the quantum spacetime in string theory, and when does it start showing up? Near the string, or Planck scale, or species scale? Is it noncommutative geometry or the other approaches mentioned in otherNG? Is it related to DFT DFT? See also ^[27].
Understanding black hole singularities, initial singularities, and causality within string theory. Do conjectures like “cosmic censorship” and “chronology protection” hold true within string theory? String theory is often well-behaved at naked singularities. Is there any version of cosmic censorship conjecture that is consistent with string theory?
Is the superstring weakly coupled? ^[28]
Understanding QFT more properly using knowledge from string theory. Example: Developing techniques to understand interacting $6D$ SCFTs that might not have a Lagrangian description. See section 6D.

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