String Theory Journal Club
sala 2.25, ul. Pasteura 5
2025-02-28 (17:00) 
Sridip Pal (Caltech)
The Conformal Bootstrap: Non-perturbative explorations of Quantum Systems
Conformal field theories (CFTs) are special landmarks in the space of Quantum field theories. They sit at the fixed points of renormalization group flow and describe the physics of systems at critical points. CFTs provide an exact definition of quantum gravity via the holographic principle. Remarkably, the high-energy spectrum of a CFT encodes the physics of black holes, revealing deep insights into quantum gravity.
A powerful non-perturbative approach to understanding CFTs is the conformal bootstrap, which exploits fundamental consistency principles—locality, unitarity, and crossing symmetry—to extract exact results. In this talk, I will demonstrate how the analytical conformal bootstrap yields rigorous universal results about key observables in CFTs, with striking applications to black hole physics and entanglement entropy in statistical mechanics.
Furthermore, I will unveil a novel and profound connection between hyperbolic geometry and the conformal bootstrap. Surprisingly, the same bootstrap techniques that constrain CFTs provide nearly optimal bounds on the spectrum of the Laplacian on compact hyperbolic manifolds—offering a fresh perspective on these spaces as toy models for quantum chaos. This unexpected link opens new avenues for understanding both quantum chaotic systems and the mathematics of hyperbolic manifolds, illustrating the power of modern theoretical physics to bridge seemingly distant domains.
Zoom: https://uw-edu-pl.zoom.us/j/99356019605?pwd=9imwam3ZNLBME7iJZDG0bJcmwvoE3S.1
A powerful non-perturbative approach to understanding CFTs is the conformal bootstrap, which exploits fundamental consistency principles—locality, unitarity, and crossing symmetry—to extract exact results. In this talk, I will demonstrate how the analytical conformal bootstrap yields rigorous universal results about key observables in CFTs, with striking applications to black hole physics and entanglement entropy in statistical mechanics.
Furthermore, I will unveil a novel and profound connection between hyperbolic geometry and the conformal bootstrap. Surprisingly, the same bootstrap techniques that constrain CFTs provide nearly optimal bounds on the spectrum of the Laplacian on compact hyperbolic manifolds—offering a fresh perspective on these spaces as toy models for quantum chaos. This unexpected link opens new avenues for understanding both quantum chaotic systems and the mathematics of hyperbolic manifolds, illustrating the power of modern theoretical physics to bridge seemingly distant domains.
Zoom: https://uw-edu-pl.zoom.us/j/99356019605?pwd=9imwam3ZNLBME7iJZDG0bJcmwvoE3S.1