Scientific Series

I'll discuss four-point functions of CFT operators with infinite scaling dimension, which arise ubiquitously in both holographic and non-holographic CFTs in general dimension, as well as in the flat space limit of rigid QFTs on AdS. The space of these correlators is poorly understood, due to both their computational complexity and inaccessibility through standard bootstrap techniques. To navigate these challenges, I'll introduce a rigorous framework for extracting well-defined ``maximally heavy observables,'' which are analogous to intrinsic quantities describing statistical systems in the thermodynamic limit. These observables are highly constrained by crossing symmetry and unitarity, and shed light on the emergence of bulk locality through dynamical phase transitions. I'll relate this framework to torus partition functions at large central charge, and work out illustrative examples in generalized free theories and the four-point function of maximal giant gravitons in planar $\mathcal{N}=4$ SYM.

Formulations of gravity as a constrained topological theory not only help us understand its variables and symmetries, but also are especially useful for quantization. In the first part of this talk, I will present the EPRL (Engle-Pereira-Rovelli-Livine) model, which is a spinfoam quantization of the four-dimensional Einstein-Cartan-Holst gravity that relies exactly on its relation to a topological theory. Namely, it transforms the simplicity constraints, distinguishing the continuum gravitational theory from its topological counterpart, into a condition on states in the Hilbert space, which is imposed after quantization. The second part of the talk will be concerned with my ongoing work on a different formulation of general relativity, which emerges from a topological theory through a different mechanism: gauging the Lorentz symmetry. I will overview the relationship between these theories in the continuum, as well as mention the current progress in their discretization.

Gibbons and Hawking proposed that the Euclidean gravity path integral with periodic boundary conditions in time computes the thermal partition sum of gravity. As a corollary, they argued that a derivative of the associated free energy with respect to the Euclidean time period computes gravitational entropy. Why is this interpretation correct?  That is, why does this path integral compute a trace over the Hilbert space of quantum gravity?   I will show that the quantity computed by the Gibbons-Hawking path integral is equal to an a priori different object -- an explicit thermal trace over the Hilbert space spanned by states produced by the Euclidean gravity path integral. I will explain that this follows if the Hilbert space with two boundaries factorizes into a product of two single boundary Hilbert spaces.  To show the latter I will develop a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. I will use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space, from which our main result will follow.

Tidal disruption events — where an unfortunate star is destroyed by a previously quiescent supermassive black hole — offer a unique probe of the low mass end of the supermassive black hole population. Recent observational advances have lead to the discovery of ~100 such events, many of which are comprehensively followed up across the entire electromagnetic spectrum. I will discuss how time-dependent relativistic accretion theory can be used to understand this multi wavelength emission from optical through X-ray energies, and how this theory allows tidal disruption events to act as probes of the massive black hole population. I will present current constraints on the occupation fraction of intermediate mass black holes, and look forward to what can be expected in the LSST era.

Defects and boundaries play an important role in a wide range of physical contexts, from particle physics to critical phenomena. In this talk, I will discuss how bulk symmetries can be realized in subtle ways in the presence of such impurities, introducing the concepts of symmetry reflecting defects and defect anomalies. I will focus on two main applications. First, I will demonstrate how these symmetry considerations can impose strong constraints on the long-distance dynamics. Second, I will show how they provide a natural explanation for scattering processes whose outgoing states appear to carry unusual quantum numbers. These phenomena can be understood and systematically predicted from topological considerations, in a variety of examples including massive theories.

I will describe new ideas relating quantum chaos to the complexity of time evolution.  One approach treats physical time evolution as a quantum computation, and bounds the smallest quantum circuit that can simulate this evolution.  The second approach quantifies how ergodically and rapidly a quantum state explores the accessible part of the system's Hilbert space.  I will illustrate how these measures separate integrable and chaotic quantum systems by considering examples including spin chains, quantum billiards, quantum many body systems, and Random Matrix Theory.  I will end by describing an application of these methods to a conjecture that geometrizes complexity in quantum gravity, and will comment on the relevance of these ideas for the break down of effective field theory near spacelike singularities.

Interacting fermions exhibit a rich landscape of surface defects. We investigate novel surface critical phenomena in systems governed by the three-dimensional Gross–Neveu–Yukawa CFT. In particular, we obtain exact infrared solutions for a class of defect renormalization group flows and demonstrate how various fermionic anomalies are encoded in the resulting surface dynamics. We also comment on the emergent topology and geometry in the defect coupling space.