Consistent Kaluza-Klein truncations to maximal supergravities in $D=2$ spacetime dimensions remain "terra incognita". Using techniques based on exceptional geometry, I will present the scalar potential of all gauged supergravities that admit a consistent embedding in ten or eleven dimensions. This provides the first general expression for a multitude of theories with an interesting structure of vacua, covering potentially many new $AdS_2$ cases. As a concrete example, I will discuss the consistent truncation of IIA supergravity on the eight-sphere to $SO(9)$ gauged maximal supergravity. Fluctuations around its supersymmetric $SO(9)$-invariant vacuum holographically describe the dynamics of interacting $D0$-branes.

We construct infinite-dimensional R-matrices that generalise the relativistic scattering of massless modes with the same chirality on $AdS_2$ near the Berestein-Maldacena-Nastase vacuum. We show that the infrared limit of the R-matrices reproduces finite-dimensional scattering of massless modes on $AdS_2$, from which the R-matrices borrow modified braiding unitary. We also prove that the R-matrices enjoy an infinite-dimensional symmetry superalgebra that embeds that of $AdS_2$. Finally, we verify that the R-matrices are also invariant under crossing symmetry.

Error-correcting codes are known to define chiral 2d lattice CFTs where all the $U(1)$ symmetries are enhanced to $SU(2)$. In this paper, we extend this construction to a broader class of length-$n$ codes which define full (non-chiral) CFTs with $SU(2)^n$ symmetry, where $n=c+ \bar c$. We show that codes give a natural discrete ensemble of 2d theories in which one can compute averaged observables. The partition functions obtained from averaging over all codes weighted equally is found to be given by the sum over modular images of the vacuum character of the full extended symmetry group, and in this case the number of modular images is finite. This averaged partition function has a large gap, scaling linearly with $n$, in primaries of the full $SU(2)^n$ symmetry group. Using the sum over modular images, we conjecture the form of the genus-2 partition function. This exhibits the connected contributions to disconnected boundaries characteristic of wormhole solutions in a bulk dual.

The principle of the holography of information states that in a theory of quantum gravity a copy of all the information available on a Cauchy slice is also available near the boundary of the Cauchy slice. This redundancy in the theory is already present at low energy. In the context of the AdS/CFT correspondence, this principle can be translated into a statement about the dual conformal field theory. We carry out this translation and demonstrate that the principle of the holography of information holds in bilocal holography.