Abstract: We introduce a framework for quantifying random matrix behavior of 2d CFT and AdS_3 quantum gravity that is manifestly compatible with conformal and modular invariance. We explain what it means to isolate the chaotic part of the Virasoro primary spectrum of a given theory. This leads to a 2d CFT trace formula, analogous to the Gutzwiller trace formula for … Read More
Abstract: Mirror symmetry for 3d N=4 SUSY QFTs has recently received much attention in geometry and representation theory. Theories within this class give rise to interesting moduli spaces of vacua, whose most relevant components are called the Higgs and Coulomb branches. Nakajima initiated the mathematical study of Higgs branches in the 90s; since then, their geometry has been pivotal in … Read More
The Hawking-Page phase transition in holography is associated with the emergence of new symmetries and dynamical properties of correlators. Above the transition point: (1) Correlators cluster in time (Maldacena’s information loss) (2) There exists a coarse-grained entropy that grows monotonically in time (Second law) (3) A large class of correlators decay exponentially (Quasi-normal modes) (4) There is an emergent approximate … Read More
Abstract: “We link several constructions of vertex operator algebras (VOA) in supersymmetric QFT. One is the SCFT/VOA correspondence of Beem et al, identifying VOA inside the protected sector of a 4d N=2 SCFT. Using the Omega-background approach to the SCFT/VOA, and compactifying the 4d theory on the infinite cigar geometry, we relate this to the construction of boundary VOAs in … Read More
Abstract — Boundaries in gravitational systems are essential for defining observables. When an asymptotic boundary is absent, finite size boundaries may be employed to get a grasp of various properties of the system. In this presentation I will discuss how introducing a boundary in the static patch of de Sitter space helps understanding its thermodynamics, specifically entropy derivation and proper … Read More
Abstract: My talk is based on the joint project with Lev Rozansky. I will explain how we rigorously construct 3D TQFT, which is a KRS theory with targets Hilbert scheme of points on a plane. Defects in the last theory encode a knot in the three-space and we rediscover the HOMFLY-PT homology of a link as a part of the … Read More
Abstract: The averaged null energy operator is a light-ray integral of the null energy. This operator is known to be closely tied to causality in AdS/CFT, to deformations of the modular Hamiltonian in quantum field theory, and to the Lorentzian inversion formula in CFT. I will discuss a new connection between averaged null energy and the monotonicity of the renormalization … Read More