Physics Colloquium: “The Conformal Bootstrap: Road to Quantum Gravity and Chaos”

The Syracuse University Department of Physics is pleased to welcome Sridip Pal, Sherman Fairchild Postdoctoral Scholar Research Associate at the Burke Institute for Theoretical Physics at Caltech, for his talk titled, “The Conformal Bootstrap: Road to Quantum Gravity and Chaos.”

Before joining Caltech, Pal was a Founders’ Circle member at the Institute for Advanced Study at Princeton (2019–2022). He earned his Ph.D. from the University of California, San Diego, in 2019. Pal’s research focuses on conformally invariant Quantum Field Theories (Conformal Field Theories, or CFTs) and spans a diverse range of topics—including black holes, quantum gravity, string theory, and quantum information-inspired quantities—as well as connections to analytic number theory and the spectral geometry of hyperbolic manifolds. Pal’s research envisions advancing our understanding of the quantum nature of black holes, gravity and the universal features of strongly interacting chaotic quantum systems with conformal symmetry.

Abstract: 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.