C4

Since Hawking first discovered that black holes radiate, the evaporation of black holes has been a subject of great interest. In this talk, based on [2411.03447], we review some recent results about the evaporation of charged (Reissner-Nordström) black holes. We consider in particular the difference between neutral and charged particle emission, and explain how this drives the black hole near extremality, as well as how evaporation is then changed in that limit.

I will discuss the preprint arXiv:2409.18130 describing an interesting connection between 4d N=2 SCFTs and 2d chiral CFTs (alias: Vertex Operator Algebras) by way of 3d EFTs.

Celestial holography posits that the 4D S-matrix may be calculated holographically by a 2D conformal field theory. However, bulk translation invariance forces low-point massless celestial amplitudes to be distributional, which is an unusual property for a 2D CFT. In this talk, I show that translation-invariant MHV gluon amplitudes can be extracted from smooth 'leaf' amplitudes, where a bulk interaction vertex is integrated only over a hyperbolic slice of spacetime. After describing gluon leaf amplitudes' soft and collinear limits, I will show that MHV leaf amplitudes can be generated by a simple 2D system of free fermions and the semiclassical limit of Liouville theory, showing that translation-invariant, distributional amplitudes can be obtained from smooth correlation functions. An important step is showing that, in the semiclassical limit of Liouville theory, correlation functions of light operators are given by contact AdS Witten diagrams. This talk is based on a series of papers with Atul Sharma, Andrew Strominger, and Tianli Wang [2312.07820, 2402.04150,2403.18896]. 

I will review recent progess on a topic of common interest to many
physicists https://www.arxiv.org/abs/2410.12043. Time permitting, I will
also comment about new sum rules for protected operators along RG flows:
https://arxiv.org/pdf/2409.09006. 

One recent(ish) development in classical black hole thermodynamics is the inclusion of vacuum energy (cosmological constant) in the form of thermodynamic pressure. New thermodynamic phase transitions emerge in this extended phase space, beyond the usual Hawking—Page transition. This allows us to understand black holes from the viewpoint of chemistry in terms of concepts such as Van Der Waals fluids, reentrant phase transitions and triple points. I will review these developments and discuss the dictionary between the bulk laws and those of the dual CFT.
 

We discuss the trace problem and stable rank for tracialy complete C*-algebras

In the category of operator systems, identification comes via complete order isomorphisms, and so an operator system can be identified with a C*-algebra without itself being an algebra. So, when is an operator system a C*-algebra? This question has floated around the community for some time. From Choi and Effros, we know that injectivity is sufficient, but certainly not necessary outside of the finite-dimensional setting. In this talk, I will give a characterization in the separable nuclear setting coming from C*-encoding systems. This comes from joint work with Galke, van Lujik, and Stottmeister.

The Cuntz semigroup of a C*-algebra is an ordered monoid consisting of equivalence classes of positive elements in the stabilization of the algebra.  It can be thought of as a generalization of the Murray-von Neumann semigroup, and records substantial information about the structure of the algebra.  Here we examine the set of positive elements having a fixed equivalence class in the Cuntz semigroup of a simple, separable, exact and Z-stable C*-algebra and show that this set is path connected when the class is non-compact, i.e., does not correspond to the class of a projection in the C*-algebra.  This generalizes a known result from the setting of real rank zero C*-algebras.