# Automorphic Spectra and the Conformal Bootstrap

@inproceedings{Kravchuk2021AutomorphicSA, title={Automorphic Spectra and the Conformal Bootstrap}, author={Petr Kravchuk and Dalimil Maz{\'a}{\vc} and Sridip Pal}, year={2021} }

We point out that the spectral geometry of hyperbolic manifolds provides a remarkably precise model of the modern conformal bootstrap. As an application, we use conformal bootstrap techniques to derive rigorous computer-assisted upper bounds on the lowest positive eigenvalue λ1(X) of the Laplace-Beltrami operator on closed hyperbolic surfaces and 2-orbifolds X. In a number of notable cases, our bounds are nearly saturated by known surfaces and orbifolds. For instance, our bound on all genus-2…

## 6 Citations

Bootstrapping closed hyperbolic surfaces

- MathematicsJournal of High Energy Physics
- 2022

Abstract
The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions and holomorphic s-differentials satisfy certain consistency conditions on closed hyperbolic…

Calabi-Yau metrics, CFTs and random matrices

- Mathematics
- 2022

Calabi–Yau manifolds have played a key role in both mathematics and physics, and are particularly important for deriving realistic models of particle physics from string theory. Unfortunately, very…

Fast Arbitrary Precision Floating Point on FPGA

- Computer ScienceArXiv
- 2022

This work shows how APFP multiplication on compile- time ﬁxed-precision operands can be implemented as deep FPGA pipelines with a recursively deﬁned Karatsuba decomposition on top of native DSP multiplication, and applies this architecture to general matrix-matrix multiplication.

Selberg trace formula and hyperbolic band theory

- Mathematics
- 2022

We apply Selberg’s trace formula to solve problems in hyperbolic band theory, a recently developed extension of Bloch theory to model band structures on experimentally realized hyperbolic lattices.…

Snowmass White Paper: The Analytic Conformal Bootstrap

- Physics
- 2022

The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general…

Snowmass White Paper: The Numerical Conformal Bootstrap

- Mathematics
- 2022

: We give a brief overview of the status of the numerical conformal bootstrap.

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