# A One-Loop Test of the near-AdS$_2$/near-CFT$_1$ Correspondence

## TL;DR

This paper investigates quantum fluctuations in near-AdS$_2$ black holes, showing that logarithmic corrections are governed by quadratic holomorphic differentials and aligning with SYK model results, with implications for 2D dilaton gravity.

## Contribution

It demonstrates that quantum corrections in near-AdS$_2$ black holes are determined by quadratic holomorphic differentials, extending understanding of quantum effects in 2D gravity.

## Key findings

- Logarithmic corrections are governed by quadratic holomorphic differentials.
- Quantum-corrected partition function matches SYK model results.
- Results generalize to other 2D dilaton gravity theories.

## Abstract

We analyze quantum fluctuations around black hole solutions to the Jackiw-Teitelboim model. We use harmonic analysis on Euclidean AdS$_2$ to show that the logarithmic corrections to the partition function are determined entirely by quadratic holomorphic differentials, even when conformal symmetry is broken and harmonic modes are no longer true zero modes. Our quantum-corrected partition function agrees precisely with the SYK result. We argue that our effective quantum field theory methods and results generalize to other theories of two-dimensional dilaton gravity.