Bootstrapping Universal Asymptotics of Conformal Field Theory via Thermal Effective Action

Author: Lee, Jaeha

Year: 2026

Degree: Dissertation (Ph.D.)

Advisor: Ooguri, Hirosi

Committee Members: Simmons-Duffin, David; Ooguri, Hirosi; Yu, Tony Yue; Cheung, Clifford W.

Option: Physics

DOI: 10.7907/00ej-3z79

Abstract

This thesis explores the asymptotic behavior of Conformal Field Theory (CFT) data at high energies using thermal effective action methods. Well-established results from two dimensions like Cardy formula, OPE coefficient asymptotics, and spin-refined partition function are extended to higher-dimensional theories.

In the first part (Chapter 2), we study the asymptotic density of states formula to CFTs with continuous symmetries. Building on recent work that established the formula for finite groups, we derive universal results for compact Lie groups G. Together with checking on various theories, the formula is explained with thermal effective action.

In the second part (Chapter 3), we develop the systematic exploration of thermal effective action methods for Cardy formula for the general dimension. Additionally, by introducing the "hot spot hypothesis," shrinking circles in complex geometries act as local thermal circles, and we extends the applicability of thermal effective action from simple fibrated manifolds to diverse geometries with extreme focusing structures, opening new avenues for computing CFT observables.

In the third part (Chapter 4), we uncover a fractal-like structure in spin-refined partition functions in higher dimension using a cutting and gluing technique, decomposing the geometry into successive quotients and identifying Kaluza-Klein vortex defects. This reveals how thermal effective action methods remain robust even for discrete geometries and rational rotations.

Our methods are purely field-theoretic and apply to both holographic and non-holographic theories. The results have implications for understanding black hole microstates in AdS/CFT, the statistics of OPE coefficients, and potential extensions of bootstrap axioms beyond traditional crossing symmetry. The thermal effective action framework studied here provides a systematic approach to computing high-energy asymptotics in CFTs, opening new avenues for exploring the structure of conformal field theories in dimensions greater than two.

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