Local Langlands Duality and a Duality of Conformal Field Theories

TL;DR

This paper reveals a deep connection between local Langlands duality and T-duality in quantum gravity, unifying them through the local Fourier transform's symmetry principles in arithmetic and geometric contexts.

Contribution

It demonstrates that local Langlands duality and T-duality are manifestations of the same underlying symmetry principle via the local Fourier transform.

Findings

Local Fourier transform unifies arithmetic and geometric Langlands parameters.

Local Langlands duality and T-duality originate from the same symmetry principle.

The paper provides a conceptual framework linking number theory and quantum gravity.

Abstract

We show that the numerical local Langlands duality for GL_n and the T - duality of two-dimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its l-adic and complex incarnation gives rise to symmetries of arithmetic and geometric local Langlands parameters.