L6

Flat space holography, if there really is such a thing, is intimately related to Carrollian geometry. I will give an introduction to Carrollian geometry, and discuss how many Carrollian spaces of interest arise as homogeneous spaces of the Poincaré group. Finally, I will discuss the construction of Cartan geometries modelled on these spaces.

The canonical example of AdS/CFT relates N=4 SYM in 4d to supergravity on AdS5 x S5 by considering a stack of D3-branes. A natural question then emerges: what about considering other Dp-branes? The worldvolume theory is again SYM but is not conformal anymore, while the supergravity dual is now only conformally AdS. Despite these differences, some control remains, and some inspiration from the p=3 case can be sought. In this talk, I will review this setup and discuss the recent results of [2503.18770] and [2503.14685] regarding the computation of correlation functions.

For this JC, I will review the recently much debated puzzles that arise in holographic systems with baby universes. After describing the original set-up of Antonini-Sasieta-Swingle, I will explain the paradox raised by Antonini-Rath, which suggests the existence of a single CFT state that can have two distinct holographic descriptions in the bulk: one with a closed baby universe and one without. I will discuss various proposed resolutions of this puzzle, which may (or may not) require us to rethink the holographic dictionary in AdS/CFT.

I will review an elegant, theory-independent argument that proves the existence of exactly marginal operators in the presence of a conformal manifold. The proof relies on a few technical assumptions, which I will discuss in detail. The rest of the discussion will be phrased in terms of conformal interfaces separating two CFTs on the conformal manifold, which we take as an opportunity to discuss the fundamentals of defect CFTs. The overarching topic into which this result fits is that of proving certain (AdS) swampland conjectures from CFT principles.

Given a quantum Hamiltonian, represented as an $N \times N$ Hermitian matrix $H$, we derive an expression for the largest Lyapunov exponent of the classical trajectories in the phase space appropriate for the dynamics induced by $H$. To this end we associate to $H$ a graph with $N$ vertices and derive a quantum map on functions defined on the directed edges of the graph. Using the semiclassical approach in the reverse direction we obtain the corresponding classical evolution (Liouvillian) operator. Using ergodic theory methods (Sinai, Ruelle, Bowen, Pollicott\ldots) we obtain closed expressions for the Lyapunov exponent, as well as for its variance. Applications for random matrix models will be presented.

The capacity of a set is a classical notion in potential theory and it is a measure of the size of a set as seen by a random walk or Brownian motion. Recently Zhu defined the notion of branching capacity as the analogue of capacity in the context of a branching random walk. In this talk I will describe joint work with Amine Asselah and Bruno Schapira where we introduce a notion of capacity of a set for critical bond percolation and I will explain how it shares similar properties as in the case of branching random walks.