Arithmetic Modular Kernels and a No-Go for Pure $\mathrm{AdS}_3$ Gravity

ADS seminar

Organizer：

数学物理团队

Speaker：

Miguel Tierz (SIMIS)

Time：

Wed., 13:30 - 14:30

Dec. 24, 2025

Venue：

B725, Shuangqing Complex Building

Title:

Arithmetic Modular Kernels and a No-Go for Pure $\mathrm{AdS}_3$ Gravity

Abstract:

I will present an analytic approach to the 2D modular bootstrap based on explicit $ST^{n}S$ modular kernels for non-rational Virasoro CFTs. On integer ``width'' slices, the Mordell-integral representation reduces to finite quadratic Gauss sums with Weil phases, yielding a finite-dimensional basis of elementary spectral profiles. This enables the construction of explicit positive window functionals without semidefinite programming. As applications, I will describe a rigorous obstruction to large gaps in diagonal/spinless modular crossing and an elliptic-point odd-spin mechanism---via a strictly positive Mordell surplus at $\rho=e^{2\pi i/3}$---that rules out Virasoro-only pure $\mathrm{AdS}_3$ gravity with a primary gap above the BTZ threshold.