Week 27.05.2024 – 02.06.2024

In recent years, there has been a lot of interest in a generalized notion of symmetry, obtained by relaxing the invertibility constraint and/or allowing symmetry operators to act on submanifolds rather than the full space. The mathematical structure underlying these generalized symmetries is provided by (higher) category theory, but it turns out that in the lattice setting, the abstract categorical formulation can be broken down to concrete tensor network operators that realize these generalized symmetries. In a certain sense, these tensor network operators provide the lattice representation theory of these generalized symmetries. As an application, I will explain how this representation theory provides a systematic, constructive theory for duality transformations on the lattice. Additionally, I will explain how dualities and generalized symmetries can be turned into unitary operators by including an ancillary degree of freedom, turning them into completely positive maps.

Detecting local Non-Gaussianity provides valuable insights into the early universe's particle composition. Interactions between the inflaton and light particles yield distinctive signatures, potentially observable in upcoming surveys. However, addressing IR divergences in light fields on de Sitter spacetimes requires careful treatment. Stochastic inflation offers a solution, but its relationship with perturbative computations remains unclear. In this presentation, we establish a precise connection between perturbation theory and stochastic formalism using the wavefunction formalism. We extend this analysis to multifield inflation models and clarify recent non-perturbative findings from stochastic inflation through their compatibility with perturbation theory calculations.

I will present a method for deriving the microscopic entropy of a very general class of supersymmetric, rotating, and accelerating black holes in AdS(4). This is achieved by analyzing the large-N limit of the spindle index.

Recent progress has provided methods to compute and match finite N (supersymmetric) partition functions on both sides of the holographic duality within string and M-theory. An advent that allows for interesting opportunities in the study of quantized strings and branes in curved backgrounds. I will discuss \mathcal{N}=4 SYM, its S-fold cousins, and how localization allows to compute their supersymmetric partition functions analytically as a function of N. We will subsequently discuss some peculiar features of these S-folds; such as their seemingly non-compact conformal manifold, and the fact that their partition functions can be expanded in fluctuating gravitons and D3-branes, very much a-like the giant graviton expansion in \mathcal{N}=4 SYM, even though a clear index interpretation is absent on the QFT side.

Asymptotically-flat spacetimes play a central role in the study of gravitational radiation. They are also the arena which enables to understand the relationship between asymptotic symmetries, soft graviton theorems, and memory effects. While this relationship is well understood at leading order in terms of BMS symmetries and flux-balance laws for the mass and angular momentum, the subleading structure has only begun to be investigated recently. In this talk we will present a study of this subleading structure using the Newman-Penrose formalism. This enables to identify an infinite tower of quasi-conserved charges generating an intriguing algebraic structure.